Question

Y= a^(7x+4 ) find dy/dx​

Answer 1

Step-by-step explanation:

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Answer 2

$\displaystyle \sf \frac{dy}{dx} = 7{a}^{(7x + 4)} log a$

Given :

$\displaystyle \sf y = {a}^{(7x + 4)}$

To find :

$\displaystyle \sf \frac{dy}{dx}$

Solution :

Step 1 of 2 :

Write down the given function

Here the given function is

$\displaystyle \sf y = {a}^{(7x + 4)}$

Step 2 of 2 :

Find the derivative

$\displaystyle \sf y = {a}^{(7x + 4)}$

Differentiating both sides with respect to x we get

$\displaystyle \sf \frac{dy}{dx} = \frac{d}{dx} \bigg({a}^{(7x + 4)}\bigg)$

$\displaystyle \sf{ \implies }\frac{dy}{dx} = {a}^{(7x + 4)}loga. \frac{d}{dx} \bigg({(7x + 4)}\bigg)\: \: \: \bigg[ \: \because \: \frac{d}{dx} \bigg({a}^{x}\bigg)={a}^{x} loga \bigg]$

$\displaystyle \sf{ \implies }\frac{dy}{dx} = {a}^{(7x + 4)}loga \times 7$

$\displaystyle \sf{ \implies }\frac{dy}{dx} = 7{a}^{(7x + 4)}loga$

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