Question

If y= e2x then value of dy/dx for
x=1/2 is​

Answer 1

Answer:

2e^2x

Step-by-step explanation:

By apllying the formula of differentiation , weget the answer.

For clarification, refer to the picture☺

Answer 2

$\displaystyle\boxed{[\dfrac{dy}{dx}]_{x=\dfrac{1}{2}}=2e}$

Tips:

We must know a derivative formula before we solve the problem,

$\dfrac{d}{dx}(e^{mx})=m\:e^{mx}$

Step-by-step explanation:

Given, $y=e^{2x}$

Now, differentiating both sides with respect to $x$, we get

$\displaystyle \dfrac{dy}{dx}=\dfrac{d}{dx}(e^{2x})$

$\Rightarrow \dfrac{dy}{dx}=2\:e^{2x}$ ... ... (1)

When $x=\dfrac{1}{2}$, from (1), we get

$[\dfrac{dy}{dx}]_{x=\dfrac{1}{2}}=2\:e^{2\times\dfrac{1}{2}}$

$=2\:e^{1}$

$=2e$

#SPJ3