Question

Open challenge......... ​

Answer 1

QUESTION :–

• If y = $\frac{1}{ \sqrt{x} } + \frac{2}{ {x}^{ \frac{3}{2} } } - \frac{4}{ {x}^{ \frac{5}{2} } }$ then find $\frac{dy}{dx}$

ANSWER :–

GIVEN :–

A function y = $\frac{1}{ \sqrt{x} } + \frac{2}{ {x}^{ \frac{3}{2} } } - \frac{4}{ {x}^{ \frac{5}{2} } }$

TO FIND :–

$\frac{dy}{dx} = ?$

SOLUTION :–

• Given function –

$\\ y = \frac{1}{ \sqrt{x} } + \frac{2}{ {x}^{ \frac{3}{2} } } - \frac{4}{ {x}^{ \frac{5}{2} } }$

• We should write this as –

$\\ \implies y = {x}^{ - \frac{1}{2} } + 2 {x}^{ - \frac{3}{2} } - 4 {x}^{ - \frac{5}{2}}$

• Now Differentiate with respect to 'x' –

$\\ \implies \frac{dy}{dx} = - \frac{1}{2} {x}^{ - \frac{3}{2} } + 2( - \frac{3}{2} ) {x}^{ - \frac{5}{2} } - 4( - \frac{5}{2} ) {x}^{ - \frac{7}{2} }$

$\\ \implies \frac{dy}{dx} = - \frac{1}{2} {x}^{ - \frac{3}{2} } - 3 {x}^{ - \frac{5}{2} } + 10 {x}^{ - \frac{7}{2} }$

Used formula :–

$\\ (1) \frac{d({x}^{n})}{dx} = n {x}^{n - 1}$