If y = 5e^{2x} + \cos(4x), find the value of \frac{dy}{dx} at x = 0. — JAMB UTME

If $y = 5e^{2x} + \cos(4x)$ , find the value of $\frac{dy}{dx}$ at $x = 0$ .

Answer: 10

Differentiating

y = 5e^{2x} + \cos(4x)

with respect to

x

yields

\frac{dy}{dx} = 10e^{2x} - 4\sin(4x)

. Substituting

x = 0

gives

10e^0 - 4\sin(0) = 10(1) - 0 = 10

Differentiate

y = 5e^{2x} + \cos(4x)

with respect to

x

\frac{dy}{dx} = 10e^{2x} - 4\sin(4x)

The derivative of

e^{ax}

a e^{ax}

and the derivative of

\cos(ax)

-a \sin(ax)

Evaluate the derivative at

x = 0

Substitute

x = 0

into

10e^{2x} - 4\sin(4x)

to obtain

10(1) - 4(0) = 10

Differentiation of exponential and trigonometric functions

Question