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d)
y=e^(7x)

d) $y=e^{7 x}$

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Find derivatives using the chain rule II

Full solution

Q. d)

y=e^{7 x}

Identify function and derivative: Identify the function and the type of derivative needed. $\newline$ We need to find the derivative of $y = e^{7x}$ with respect to $x$ .
Apply chain rule: Apply the chain rule for differentiation. $\newline$ The chain rule states that if $y = e^{u}$ , then $\frac{dy}{dx} = e^{u} \cdot \frac{du}{dx}$ . $\newline$ Here, $u = 7x$ , so $\frac{du}{dx} = 7$ .
Perform differentiation: Perform the differentiation using the chain rule. $\frac{dy}{dx} = e^{7x} \cdot 7$ .

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