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Popular >

derivative of f(x)=(x^3+4)e^x

Solution

derivative of

f (x) = (x^{3} + 4) e^{x}

Solution

3 x^{2} e^{x} + e^{x} (x^{3} + 4)

Solution steps

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

Apply the Product Rule:

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

f = x^{3} + 4, g = e^{x}

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

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

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

= 3 x^{2} e^{x} + e^{x} (x^{3} + 4)

Graph

Popular Examples

integral of (x^2+4)/(x+1)

\int \frac{x ^{2} + 4}{x + 1} d x

sum from n=0 to infinity of 3(x/4)^n

n = 0 \sum \infty 3 (\frac{x}{4})^{n}

tangent of f(x)= 1/(x-5),\at x=10 tangent of

f (x) = \frac{1}{x - 5}, at x = 10

derivative of g(x)=x^2(1-7x)derivative of

g (x) = x^{2} (1 - 7 x)

derivative of ((x+7/(x-7))^5)

\frac{d}{d x} ((\frac{x + 7}{x - 7})^{5})

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(x^3+4)e^x ?
The derivative of f(x)=(x^3+4)e^x is 3x^2e^x+e^x(x^3+4)
What is the first derivative of f(x)=(x^3+4)e^x ?
The first derivative of f(x)=(x^3+4)e^x is 3x^2e^x+e^x(x^3+4)