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Popular >

derivative of e^xcos(4x)

Solution

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

Solution

e^{x} cos (4 x) - 4 e^{x} sin (4 x)

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (cos (4 x)) = - sin (4 x) \cdot 4

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

Simplify

= e^{x} cos (4 x) - 4 e^{x} sin (4 x)

Popular Examples

integral of ((x^2+24))/(x(x-2)^3)

\int \frac{( x ^{2} + 24 )}{x ( x - 2 ) ^{3}} d x

integral of x/(sqrt(25-(3-x)^2))

\int \frac{x}{25 - ( 3 - x ) ^{2}} d x

limit as x approaches 2 of-x^2+7x-2

x \to 2 lim (- x^{2} + 7 x - 2)

integral of 8x^3sin(1-x^4)

\int 8 x^{3} sin (1 - x^{4}) d x

integral of (x^{1.3}+7x^{2.5})

\int (x^{1.3} + 7 x^{2.5}) d x

Frequently Asked Questions (FAQ)

What is the derivative of e^xcos(4x) ?
The derivative of e^xcos(4x) is e^xcos(4x)-4e^xsin(4x)
What is the first derivative of e^xcos(4x) ?
The first derivative of e^xcos(4x) is e^xcos(4x)-4e^xsin(4x)