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Popular >

derivative of e^x(2x^4+3cos(x))

Solution

\frac{d}{d x} (e^{x} (2 x^{4} + 3 cos (x)))

Solution

e^{x} (2 x^{4} + 3 cos (x)) + (8 x^{3} - 3 sin (x)) e^{x}

Solution steps

\frac{d}{d x} (e^{x} (2 x^{4} + 3 cos (x)))

Apply the Product Rule:

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

f = e^{x}, g = 2 x^{4} + 3 cos (x)

= \frac{d}{d x} (e^{x}) (2 x^{4} + 3 cos (x)) + \frac{d}{d x} (2 x^{4} + 3 cos (x)) e^{x}

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

\frac{d}{d x} (2 x^{4} + 3 cos (x)) = 8 x^{3} - 3 sin (x)

= e^{x} (2 x^{4} + 3 cos (x)) + (8 x^{3} - 3 sin (x)) e^{x}

Popular Examples

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\frac{d}{d x} (- 2 x^{3} + \frac{8}{x ^{2}} - 6 x - 1)

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\int - 8 x^{3} cos (5 x^{4} + 1) d x

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\int_{- 1}^{2} (2 - 5 x + \frac{1}{2} x^{2}) d x

Frequently Asked Questions (FAQ)

What is the derivative of e^x(2x^4+3cos(x)) ?
The derivative of e^x(2x^4+3cos(x)) is e^x(2x^4+3cos(x))+(8x^3-3sin(x))e^x
What is the first derivative of e^x(2x^4+3cos(x)) ?
The first derivative of e^x(2x^4+3cos(x)) is e^x(2x^4+3cos(x))+(8x^3-3sin(x))e^x