For y = e 2x , the derivative dy/dx equals:

Answer: 2e^2x.

A 2e^2x
B e^2x
C 2x·e^2x
D e^2x/2

Correct answer: A. 2e^2x

Explanation: By the chain rule, dy/dx = e^2x·2 = 2e^2x.

f(x)=|x| is perfectly continuous at x=0 (no break, no jump), but the curve has a sharp corner there: approaching from the left gives slope -1 and from the right gives slope +1 - since these one-sided derivatives disagree, the function is not differentiable at that point.

Concept context

When a function has no breaks (continuity) and when it has a well-defined slope (differentiability), plus rules for differentiating implicit, inverse trig, exponential, log, and parametric functions.

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For y = e2x, the derivative dy/dx equals:

Concept context

More Continuity and Differentiability questions

For y = e^2x, the derivative dy/dx equals: