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# Class 11 RD Sharma Solutions – Chapter 30 Derivatives – Exercise 30.2 | Set 2

• Last Updated : 30 Apr, 2021

### (i) xsinx

Solution:

Given that f(x) = xsinx

By using the formula

We get

Using the formula

sinc – sind = 2cos((c + d)/2)sin((c – d)/2)

We get

As we know that

So,

= 2x Ã— cosx Ã— 1/2 + sinx

= x Ã— cosx + sinx

= sinx + xcosx

### (ii) xcosx

Solution:

Given that f(x) = xcosx

By using the formula

We get

= -xsinx + cosx

### (iii) sin(2x – 3)

Solution:

Given that f(x) = sin(2x – 3)

By using the formula

We get

Using the formula

sinC – sinD = 2cos{C+D}/2sin{C-D}/2

As we know that, \lim_{Î¸\to 0}\frac{sinÎ¸}{Î¸}=1 so,

= 2cos(2x – 3)

### (iv) âˆšsin2x

Solution:

Given that f(x) = âˆšsin2x

By using the formula

We get

On multiplying numerator and denominator by

we get

### (v) sinx/x

Solution:

Given that f{x} = sinx/x

By using the formula

We get

h â‡¢ 0 â‡’ h/2 â‡¢ 0 and

=

### (vi) cosx/x

Solution:

Given that f(x) = cosx/x

By using the formula

We get

### (vii) x2sinx

Solution:

Given that f(x) = x2sinx

By using the formula

We get

= 0 + [2xsinx + x2cosx]

= 2xsinx + x2cosx

### (viii)

Solution:

Given that f(x) =

By using the formula

We get

### (ix) sinx + cosx

Solution:

Given that f(x) = sinx + cosx

By using the formula

We get

= cosx – sinx

### (i) tan2x

Solution:

Given that f(x) = tan2x

By using the formula

We get

= 2tanx sec2x

### (ii) tan(2x + 1)

Solution:

Given that f(x) = tan(2x+1)

By using the formula

We get

Multiplying both, numerator and denominator by 2.

= 2sec2(2x+1)

### (iii) tan2x

Solution:

Given that f(x) = tan2x

By using the formula

We get

= 2sec22x

### (iv) âˆštanx

Solution:

Given that f(x) = âˆštanx

By using the formula

We get

On multiplying numerator and denominator by

We get

### (i)

Solution:

Given that f(x) =

By using the formula

We get

### (ii) cosâˆšx

Solution:

Given that f(x) = cosâˆšx

By using the formula

We get

Multiplying numerator and denominator by

### (iii) tanâˆšx

Solution:

Given that f(x) = tanâˆšx

By using the formula

We get

### (iv) tanx2

Solution:

Given that f(x) = tanx2

By using the formula

We get

= 2xsec2x2

### (i) -x

Solution:

Given that f(x) = -x

By using the formula

We get

= -1

### (ii) (-x)-1

Solution:

Given that f(x) = (-x)-1

By using the formula

We get

= 1/x2

### (iii) sin(x + 1)

Solution:

Given that f(x) = sin(x+1)

By using the formula

We get

= cos(x+1)

### (iv) cos(x – Ï€/8)

Solution:

We have, f(x) = cos(x – Ï€/8)

By using the formula

We get

= -sin(x + Ï€/8)

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