# Let f(x)=x^4. If a=1 and dx=ax=1/2, what is dy?

## Question:

Let {eq}f(x)=x^4 {/eq}.

If a=1 and dx=ax=1/2, what is dy?

## Differentiation:

In this question we are given by some values. Which than is used as attributes in differential function in order to calculate dy.

Initially obtain value of x from ax = c, and then replace dx and x in differential equation.

So do get required value of dy.

We have,

{eq}f(x)=x^4 {/eq}

a=1

dx = ax = 1/2

now,

ax = 1/2

=> x = \frac{1}{2}

now,

Differentiating f(x) both sides,

{eq}f'(x) = dy = 4x^3 dx {/eq}

On replacing the values,

{eq}dy = 4(\frac{1}{2})^3 (\frac{1}{2}) \\ dy = 4(\frac{1}{8}) (\frac{1}{2}) \\ {/eq}

so,

{eq}\therefore \color{blue}{ dy = \frac{1}{4} } {/eq}