Ans: In the question, the two capacitors are in parallel Net Capacitance, $C=C_{1}+C_{2}$ $$ \begin{array}{l} \mathrm{C}_{1}=\frac{\mathrm{K}_{1}...

### Differentiate

### Differentiate

### Differentiate

### Differentiate

### Differentiate

Answer : Let y = ex log (sin 2x) , z = e x and w = log (sin 2x) Formula

### Differentiate w.r.t x:

### Differentiate w.r.t x:

### Differentiate w.r.t x:

### Differentiate w.r.t x:

### Differentiate w.r.t x:

### Differentiate w.r.t x:

### 29. Differentiate w.r.t x:

### Differentiate w.r.t x: e (xsinx+cosx) Answer : Let y = e(xsinx+cosx) , z = x sin x+ cos x, m = x and w = sin x Formula

### Differentiate w.r.t x: cos (x3 . ex )

### Differentiate w.r.t x: e -5x cot 4x

### Differentiate w.r.t x: e 3x cos 2x

### Differentiate w.r.t x: e 2x sin 3x

### Differentiate w.r.t x:

### Differentiate the following with respect to x: sin x sin 2x

### Differentiate the following with respect to x: cos 3x sin 5x

### Differentiate

### Differentiate the following with respect to x:

### Differentiate the following with respect to x:

### Differentiate the following with respect to x:

### Differentiate the following with respect to x:

### Differentiate the following with respect to x:

### Differentiate the following with respect to x:

### Differentiate the following with respect to x:

### Differentiate the following with respect to x: (3 – 4x)5

### Differentiate the following with respect to x: (5 + 7x)6

### Differentiate the following with respect to x:

### Differentiate the following with respect to x:

### Differentiate the following with respect to x:

### Differentiate the following with respect to x: tan3x

### Differentiate the following with respect to x:

### Differentiate the following with respect to x: cos x3

### Differentiate the following with respect to x: cos 5x

### Differentiate the following with respect to x: sin 4x

To Find: Differentiation NOTE : When 2 functions are in the product then we used product rule i.e

### cotx (ii) secx

### Differentiate

### Differentiate

### Differentiate

Putting the above obtained values in the formula:-

### Differentiate

### Differentiate

### Differentiate

### Differentiate

### Differentiate

### Differentiate

### Differentiate

### Differentiate

### Differentiate

### Differentiate

### Differentiate

### Differentiate

### Differentiate

### Differentiate

### Differentiate

### Differentiate

### Differentiate

### Differentiate

### Differentiate

### Differentiate

### Differentiate

### Differentiate

### Differentiate:

Formula used: (i) (uv)âČ = uâČv + uvâČ (Leibnitz or product rule)

### Differentiate:(tan x + sec x) (cot x + cosec x)

Ans) (secx + tanx) (secx â cosecx) (cotx + cosecx)

### Differentiate:

To find: Differentiation of (x2 + 2x â 3) (x2 + 7x + 5) Formula used: (i) (uv)âČ = uâČv + uvâČ (Leibnitz or product rule) (ii) Putting the above obtained values in the formula :- (uv)âČ = uâČv + uvâČ [(x2...

### Differentiate:

### Differentiate:

### Differentiate:

### Differentiate:

### Differentiate:

### Differentiate:

### Differentiate

### Differentiate:

### Find the derivation of each of the following from the first principle: tan (3x + 1)

### Find the derivation of each of the following from the first principle:

### Find the derivation of each of the following from the first principle:

Now rationalizing the numerator by multiplying and divide by the conjugate

### Find the derivation of each of the following from the first principle:

Hence

### Find the derivation of each of the following from the first principle

### Find the derivation of each of the following from the first principle:

### Find the derivation of each of the following from the first principle:

### Find the derivation of each of the following from the first principle:

Now rationalizing the numerator by multiplying and divide by the conjugate

### Find the derivation of each of the following from the first principle:

Now rationalizing the numerator by multiplying and divide by the conjugate

### Find the derivation of each of the following from the first principle:

We need to find the derivative of f(x) i.e. fâ(x) We know that, Now rationalizing the numerator by multiplying and divide by the conjugate of

### Find the derivation of each of the following from the first principle:

We need to find the derivative of f(x) i.e. fâ(x) We know that, Now rationalizing the numerator by multiplying and divide by the conjugate of

### Find the derivation of each of the following from the first principle:

Now rationalizing the numerator by multiplying and divide by the conjugate of

### Find the derivation of each of the following from the first principle:

Now rationalizing the numerator by multiplying and divide by the conjugate of

### Find the derivation of each of the following from the first principle:

Let , We need to find the derivative of f(x) i.e. fâ(x) We know that,

### Find the derivation of each of the following from the first principle:

We need to find the derivative of f(x) i.e. fâ(x) We know that,

### Find the derivation of each of the following from the first principle:

[Add and subtract x in denominator] Hence, fâ(x) = 8x7

### Find the derivation of each of the following from the first principle: x 3 â 2×2 + x + 3

Answer : Let f(x) = x3 â 2x2 + x + 3 We need to find the derivative of f(x) i.e. fâ(x) We know that, Putting values in (i), we get Using the identities: (a + b)3 = a3 + b3 + 3ab2 + 3a2b (a + b)2 =...