Question

differentiate the following functions w.r.t.x
1) x⁵
2) x-²
3) √x
4) x√x
5)
$\frac{1}{ \sqrt{x} }$
6) 7x
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Chap : Differentiation
Class : 11th

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Answer 1

Answer:

Hi friend ✨

here is the answer ✨

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1). LetY = x⁵

Differentiating w.r.t.x we get,

$\frac{dy}{dx} = \frac{d}{dx} x {}^{5} = {5x}^{4}$

2). x-²

Let Y =

$x { }^{ - 2}$

Differentiating w.r.t.x we get,

$\frac{dy}{dx} = \frac{d}{dx} ( {x}^{ - 2} ) \\ = - 2x {}^{ - 3} \\ = \frac{ - 2}{ { x}^{3} }$

3). √x

Differentiating w.r.t.x, we get

$\frac{dy}{dx} = \frac{d}{dx} \sqrt{x} \\ = \frac{1}{ \sqrt[2]{x} }$

4). x√x

$let \: y \: = \: \sqrt[x]{x} \\ y = {x}^{ \frac{3}{2} } \\ \\ differentiating \: w.r.t.x \: we \: get \: \\ \frac{dy}{dx} = \frac{d}{dx} {x}^{ \frac{3}{2} } \\ = \frac{3}{2} {x}^{ \frac{1}{2} }$

5).

$let \: y \: = \frac{1}{ \sqrt{x} } \\ y = {x}^{ \frac{ - 1}{2} } \\ differentiating \: w.r.t.x \: we \: get \: \\ \frac{dy}{dx} = \: \frac{ - 1}{2} x {}^{ \frac{ - 3}{2} } \\ \\ = \frac{ - 1}{ {2x}^{ \frac{3}{2} } }$

6. 7x

$let \: y \: = \: 7x \: \\ differentiating \: w.r.t.x \: we \: get \\ \frac{dy}{dx} = \frac{d}{dx} 7 {}^{x} \\ = 7 {}^{x} log_{}7$

Hope it helps you ⚡