Exercise 11.5 Archives - Noon Academy

As per the given question, Let $y\;=$ \[~{{\left( \mathbf{log}\text{ }\mathbf{x} \right)}^{\mathbf{cos}\text{ }\mathbf{x}}}\] Taking log both the sides, we get

Differentiate the following functions with respect to x:
${{\left( \mathbf{log}\text{ }\mathbf{x} \right)}^{\mathbf{x}}}$

CBSE, Class 12, Differentiation, Exercise 11.5, Maths, RD Sharma

As per the given question,

Differentiate the following functions with respect to x: ${{x}^{{{\cos }^{-1}}x}}$

CBSE, Class 12, Differentiation, Exercise 11.5, Maths, RD Sharma

As per the given question,

Differentiate the following functions with respect to x:
$~{{\left( \mathbf{1}\text{ }+\text{ }\mathbf{cos}\text{ }\mathbf{x} \right)}^{\mathbf{x}}}$

CBSE, Class 12, Differentiation, Exercise 11.5, Maths, RD Sharma

As per the given question,

Differentiate the following functions with respect to x:
${{\mathbf{x}}^{\mathbf{sin}\text{ }\mathbf{x}}}$

CBSE, Class 12, Differentiation, Exercise 11.5, Maths, RD Sharma

As per the given question,

Differentiate the following functions with respect to x: ${{x}^{\frac{1}{x}}}$

CBSE, Class 12, Differentiation, Exercise 11.5, Maths, RD Sharma

As per the given question,

Differentiate the following functions with respect to x: $y=x^{n}+n^{x}+x^{x}+n^{n}$

CBSE, Class 12, Differentiation, Exercise 11.5, Maths, RD Sharma

Differentiate the following functions with respect to x: $y=e^{x}+10^{x}+x^{x}$

CBSE, Class 12, Differentiation, Exercise 11.5, Maths, RD Sharma

Differentiate the following functions with respect to x: $(v)\left(x+\frac{1}{x}\right)^{x}+x^{\left(1+\frac{1}{x}\right)}$ $\text { (vi) } e^{\sin x}+(\tan x)^{x}$

CBSE, Class 12, Differentiation, Exercise 11.5, Maths, RD Sharma

(v) (vi)

Differentiate the following functions with respect to x: $\text { (i) }\left(x^{x}\right) \sqrt{x}$ $\text { (ii) } x^{(\sin x-\cos x)}+\frac{x^{2}-1}{x^{2}+1}$

CBSE, Class 12, Differentiation, Exercise 11.5

(i) (ii)

Differentiate the following functions with respect to x: $x^{1 / x}$

CBSE, Class 12, Differentiation, Exercise 11.5, Maths, RD Sharma

Differentiate the following functions with respect to x: $\frac{{{({{x}^{2}}-1)}^{3}}(2x-1)}{\sqrt{(x-3)(4x-1)}}$

Differentiate the following functions with respect to x:
$\mathbf{y}\text{ }=\text{ }{{\mathbf{x}}^{\mathbf{n}}}~+\text{ }{{\mathbf{n}}^{\mathbf{x}}}~+\text{ }{{\mathbf{x}}^{\mathbf{x}}}~+\text{ }{{\mathbf{n}}^{\mathbf{n}}}$

Differentiate the following functions with respect to x:
$\mathbf{y}\text{ }=\text{ }{{\mathbf{e}}^{\mathbf{x}}}~+\text{ }\mathbf{1}{{\mathbf{0}}^{\mathbf{x}}}~+\text{ }{{\mathbf{x}}^{\mathbf{x}}}$

Differentiate the following functions with respect to x: $(i)\;{{\left( \mathbf{cos}\text{ }\mathbf{x} \right)}^{\mathbf{x}}}~+\text{ }{{\left( \mathbf{sin}\text{ }\mathbf{x} \right)}^{\mathbf{1}/\mathbf{x}}}$ $(ii)\;{{x}^{{{x}^{2-3}}}}+{{(x-3)}^{{{x}^{2}}}}$

Differentiate the following functions with respect to x: $(i)\;{{\left( x+\frac{1}{x} \right)}^{x}}+{{x}^{\left( 1+\frac{1}{x} \right)}}$ $(ii)\;{{\mathbf{e}}^{\mathbf{sin}\text{ }\mathbf{x}}}~+\text{ }{{\left( \mathbf{tan}\text{ }\mathbf{x} \right)}^{\mathbf{x}}}$

Differentiate the following functions with respect to x: $(i)\;{{x}^{x\cos x}}+\frac{{{x}^{2}}+1}{{{x}^{2}}-1}$ $(ii)\;{{(x\cos x)}^{x}}+{{(x\sin x)}^{\frac{1}{x}}}$

Differentiate the following functions with respect to x:
$\left( \mathbf{i} \right)\text{ }\left( {{\mathbf{x}}^{\mathbf{x}}} \right)\text{ }\surd \mathbf{x}$
$(ii){{x}^{(\sin x-\cos x)}}+\left( \frac{{{x}^{2}}-1}{{{x}^{2}}+1} \right)$

Differentiate the following functions with respect to x: ${{(\tan x)}^{\frac{1}{x}}}$

Differentiate the following functions with respect to x:
${{\left( \mathbf{tan}\text{ }\mathbf{x} \right)}^{\mathbf{1}/\mathbf{x}}}$

Differentiate the following functions with respect to x: ${{x}^{{{\sin }^{-1}}x}}$

Differentiate the following functions with respect to x:
${{(\mathbf{Si}{{\mathbf{n}}^{-\mathbf{1}}}~\mathbf{x})}^{\mathbf{x}}}$

Differentiate the following functions with respect to x:
$\mathbf{Sin}\text{ }({{\mathbf{x}}^{\mathbf{x}}})$

Differentiate the following functions with respect to x: ${{10}^{({{10}^{x}})}}$

Differentiate the following functions with respect to x:
${{\left( \mathbf{log}\text{ }\mathbf{x} \right)}^{\mathbf{log}\text{ }\mathbf{x}}}$

Differentiate the following functions with respect to x:
$\mathbf{1}{{\mathbf{0}}^{\mathbf{log}\text{ }\mathbf{sin}\text{ }\mathbf{x}}}$

Differentiate the following functions with respect to x:
$~{{\left( \mathbf{Sin}\text{ }\mathbf{x} \right)}^{\mathbf{log}\text{ }\mathbf{x}}}$

Differentiate the following functions with respect to x:
${{\mathbf{e}}^{\mathbf{x}\text{ }\mathbf{log}\text{ }\mathbf{x}}}$

Differentiate the following functions with respect to x:
${{\left( \mathbf{Sin}\text{ }\mathbf{x} \right)}^{\mathbf{cos}\text{ }\mathbf{x}}}$

Differentiate the following functions with respect to x:
$~{{\left( \mathbf{log}\text{ }\mathbf{x} \right)}^{\mathbf{cos}\text{ }\mathbf{x}}}$

Differentiate the following functions with respect to x:
${{\left( \mathbf{log}\text{ }\mathbf{x} \right)}^{\mathbf{x}}}$

Differentiate the following functions with respect to x: ${{x}^{{{\cos }^{-1}}x}}$

Differentiate the following functions with respect to x:
$~{{\left( \mathbf{1}\text{ }+\text{ }\mathbf{cos}\text{ }\mathbf{x} \right)}^{\mathbf{x}}}$

Differentiate the following functions with respect to x:
${{\mathbf{x}}^{\mathbf{sin}\text{ }\mathbf{x}}}$

Differentiate the following functions with respect to x: ${{x}^{\frac{1}{x}}}$

Differentiate the following functions with respect to x: $y=x^{n}+n^{x}+x^{x}+n^{n}$

Differentiate the following functions with respect to x: $y=e^{x}+10^{x}+x^{x}$

Differentiate the following functions with respect to x: $(v)\left(x+\frac{1}{x}\right)^{x}+x^{\left(1+\frac{1}{x}\right)}$ $\text { (vi) } e^{\sin x}+(\tan x)^{x}$

Differentiate the following functions with respect to x: $\text { (i) }\left(x^{x}\right) \sqrt{x}$ $\text { (ii) } x^{(\sin x-\cos x)}+\frac{x^{2}-1}{x^{2}+1}$

Differentiate the following functions with respect to x: $x^{1 / x}$

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