RD Chapter 30- Derivatives Ex-30.2 |
RD Chapter 30- Derivatives Ex-30.3 |
RD Chapter 30- Derivatives Ex-30.4 |
RD Chapter 30- Derivatives Ex-30.5 |

**Answer
1** :

Given:

f(x) = 3x

By using the derivative formula,

**Find the derivativeof f(x) = x ^{2} – 2 at x = 10**

**Answer
2** :

Given:

f(x) = x^{2} – 2

By using the derivative formula,

= 0 + 20 = 20

Hence,

Derivative of f(x) = x^{2} –2 at x = 10 is 20

**Answer
3** :

Given:

f(x) = 99x

By using the derivative formula,

**Answer
4** :

Given:

f(x) = x

By using the derivative formula,

**Answer
5** :

Solution:

Given:

f(x) = cos x

By using the derivative formula,

**Answer
6** :

Given:

f(x) = tan x

By using the derivative formula,

Find the derivatives of the following functions at the indicated points:

(i) sin x at x = π/2

(ii) x at x = 1

(iii) 2 cos x at x = π/2

(iv) sin 2xat x = π/2

**Answer
7** :

(i) sin x at x = π/2

Given:

f (x) = sin x

By using the derivative formula,

[Since it is ofindeterminate form. Let us try to evaluate the limit.]

We know that 1 – cos x = 2 sin^{2}(x/2)

(ii) x at x = 1

Given:

f (x) = x

By using the derivative formula,

(iii) 2 cos x at x = π/2

Given:

f (x) = 2 cos x

By using the derivative formula,

(iv) sin 2xat x = π/2

Solution:

Given:

f (x) = sin 2x

By using the derivative formula,

[Since it is of indeterminate form. We shall apply sandwich theorem to evaluate the limit.]

Now, multiply numerator and denominator by 2, we get

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