If y = e^{4x} - \sin x, what is \frac{dy}{dx}? — JAMB UTME

If $y = e^{4x} - \sin x$ , what is $\frac{dy}{dx}$ ?

4e^{4x} - \cos x

Differentiating

e^{4x}

gives

4e^{4x}

by applying the chain rule, and differentiating

-\sin x

yields

-\cos x

. Combining these terms gives the correct derivative

4e^{4x} - \cos x

Apply the sum/difference rule of differentiation.

\frac{dy}{dx} = \frac{d}{dx}(e^{4x}) - \frac{d}{dx}(\sin x)

The derivative of a difference of two terms is the difference of their individual derivatives.

Differentiate the exponential term

e^{4x}

using the chain rule.

\frac{d}{dx}(e^{4x}) = 4e^{4x}

By the chain rule, \frac{d}{dx}(e^{k x}) = k e^{k x}.

Differentiate the trigonometric term

\sin x

\frac{d}{dx}(\sin x) = \cos x

The standard derivative of

\sin x

with respect to

x

\cos x

Combine the results.

\frac{dy}{dx} = 4e^{4x} - \cos x

Subtracting the derivative of

\sin x

from the derivative of

e^{4x}

gives the final answer.

Differentiation of Exponential and Trigonometric Functions

Question