Question

Y= x . X^1/2 - 2/x^2 . Find the first derivative

Answer 1

Solution:

We are going to find the first derivative of a function $Y= x* x^{\frac 1 2} + \frac 2 {x^{2}}$

We have a formula, Derivative of $x^{n} =$ $n * x^{n-1}$

First we can rewrite the given function as Y = $x^{ 1 + \frac 1 2} + \frac 2 {x^2}$ = $x^{\frac 3 2} + 2 * x^{-2}$

since, in the multiplication, If the bases are equal , we can add the power)

( If we have a term with positive exponent at the denominator, we write that at numerator with negative exponent)

Now, the derivative of the given function

Derivative of $Y = \frac 3 2 * x^{ \frac 3 2 - 1} + 2 (-2) * x^{ - 2 -1}$

= $\frac 3 2 * x^{\frac 1 2} - 4 * x^{ -3}$

Answer: Derivative of Y =$\frac 3 2 * x^{\frac 1 2} - \frac 4 {x^{3}}$