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Popular >

derivative of e^{4x}sin(x)

Solution

\frac{d}{d x} (e^{4 x} sin (x))

Solution

e^{4 x} \cdot 4 sin (x) + cos (x) e^{4 x}

Solution steps

\frac{d}{d x} (e^{4 x} sin (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{4 x}, g = sin (x)

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

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

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

= e^{4 x} \cdot 4 sin (x) + cos (x) e^{4 x}

Popular Examples

derivative of y=5sqrt(x)derivative of

y = 5 x

integral from 0 to 1 of (1-x^2)^{0.5}

\int_{0}^{1} (1 - x^{2})^{0.5} d x

derivative of f(x)=(x^2+32sqrt(x))/8 derivative of

f (x) = \frac{x ^{2} + 32 x}{8}

(\partial)/(\partial x)(xln(z^4+x^2))

\frac{\partial}{\partial x} (x ln (z^{4} + x^{2}))

integral of cos^5(2t)

\int cos^{5} (2 t) d t

Frequently Asked Questions (FAQ)

What is the derivative of e^{4x}sin(x) ?
The derivative of e^{4x}sin(x) is e^{4x}*4sin(x)+cos(x)e^{4x}
What is the first derivative of e^{4x}sin(x) ?
The first derivative of e^{4x}sin(x) is e^{4x}*4sin(x)+cos(x)e^{4x}