First slide

Derivatives

Question

$If y = 2^{ax} and \frac{dy}{dx} = \log 256 at x = 1, then the value of a$

Moderate

A

2
B

5
C

4
D

6

Solution

$\begin{aligned} \log y = axlog 2 \\ \Rightarrow \frac{1}{y} \frac{dy}{dx} = a \log 2 \\ \Rightarrow \frac{dy}{dx} = 2^{ax} a \log 2 \end{aligned}$
$\begin{array}{l} {\frac{d y}{d x}}_{x = 1} = 2^{a} a \log 2 = 8 \log 2 \\ \Rightarrow 2^{a} \cdot a = 8 \\ \Rightarrow a = 2 \end{array}$

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