What is the derivative of $y = e^{3 \frac{x}{4}}$ $y= e^(3x/4)$ ?

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Answer 1 · 2015-08-14T06:17:07

The answer is -
$\frac{d y}{d x}$ $dy/dx$ = $\frac{3}{4}$ $3/4$ . $e^{3 \frac{x}{4}}$ $e^(3x/4)$

Understand
$e^{(s o m e exp r e s s i o n)}$ $e^((some expression))$ is to be differentiated as

(Differentiation of some expression). $e^{(s o m e exp r e s s i o n)}$ $e^((some expression))$

Apply this to the problem

Here expression is $3 \frac{x}{4}$ $3x/4$
It can be written as $\frac{3 x}{4}$ $(3x)/4$
Again it can be written as $\frac{3}{4} x$ $3/4x$

Differentiation of $\frac{3}{4} x$ $3/4x$ is $\frac{3}{4}$ $3/4$

Hence $\frac{d y}{d x}$ $dy/dx$ = $\frac{3}{4}$ $3/4$ . $e^{3 \frac{x}{4}}$ $e^(3x/4)$

What is the derivative of y=e3x4y= e^(3x/4)?