Differentiate

𝑒
7
𝑥

Question

Differentiate

𝑒
7
𝑥

BlackTom AI · Accepted Answer

The task is to differentiate the function e^{7x}. 
First, recall the standard rule for the derivative of the exponential e^{u} with respect to x: d/dx [e^{u}] = e^{u} · du/dx, where u is a function of x. 
Here, u = 7x, so du/dx = 7. 
Applying the chain rule, the derivative becomes e^{7x} · 7, which simplifies to 7 e^{7x}. 
A common pitfall is to forget the inner function’s derivative when the exponent contains x; some learners might treat the exponent as a constant or as if the derivative of the exponent were 0, but that would be incorrect. 
Another way to see it is to set u = 7x, then d/dx e^{u} = e^{u} · du/dx = e^{7x} · 7 = 7 e^{7x}. 
In this case, there are no provided answer options to evaluate, so we cannot compare alternatives, but the correct differentiated form is 7 e^{7x} based on the standard differentiation rule for exponential functions with a linear exponent.

Differentiate 𝑒 7 𝑥

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