Question

Find the derivative of y=x3/2 + logx-cosx with respect to x​

Answer 1

Answer:

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Answer 2

Concept

The formulas will use to solve the problem

1. $\frac{dx^n}{dx}=nx^{n-1}$

2. $\frac{dlogx}{dx}=\frac{1}{x}$

3. $\frac{dcosx}{dx}=sinx$

Given

The equation  $y=x^{3/2} + logx-cosx$.

Find

We have to find the derivative of the equation.

Solution

Differentiate the equation with respect to x.

$\frac{dy}{dx} =\frac{3}{2}{x}^{(\frac{3}{2}-1)}} +\frac{1}{x}-(-sinx)$

    $=\frac{3}{2} x^\frac{1}{2} +\frac{1}{x} +sinx$

   $=\frac{3}{2} \sqrt{x} +\frac{1}{x} +\sin x$

Hence the derivative is $\frac{3}{2} \sqrt{x} +\frac{1}{x} +\sin x$.