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Popular >

derivative of (x^3+1)e^x

Solution

derivative of

(x^{3} + 1) e^{x}

Solution

3 x^{2} e^{x} + e^{x} (x^{3} + 1)

Solution steps

\frac{d}{d x} ((x^{3} + 1) e^{x})

Apply the Product Rule:

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

f = x^{3} + 1, g = e^{x}

= \frac{d}{d x} (x^{3} + 1) e^{x} + \frac{d}{d x} (e^{x}) (x^{3} + 1)

\frac{d}{d x} (x^{3} + 1) = 3 x^{2}

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

= 3 x^{2} e^{x} + e^{x} (x^{3} + 1)

Popular Examples

integral of (x-2)^4 1/(sqrt(4x-x^2))

\int (x - 2)^{4} \frac{1}{4 x - x ^{2}} d x

integral of (x^2+7)e^{-x}

\int (x^{2} + 7) e^{- x} d x

(\partial)/(\partial y)(3xz^3e^{y^2})

\frac{\partial}{\partial y} (3 x z^{3} e^{y^{2}})

limit as x approaches 2 of 4x^2+x+4

x \to 2 lim (4 x^{2} + x + 4)

integral from 0 to pi/6 of (6sec^2(x))

\int_{0}^{\frac{π}{6}} (6 sec^{2} (x)) d x

Frequently Asked Questions (FAQ)

What is the derivative of (x^3+1)e^x ?
The derivative of (x^3+1)e^x is 3x^2e^x+e^x(x^3+1)
What is the first derivative of (x^3+1)e^x ?
The first derivative of (x^3+1)e^x is 3x^2e^x+e^x(x^3+1)