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Popular >

derivative of f(x)=(x^3+9)e^x

Solution

derivative of

f (x) = (x^{3} + 9) e^{x}

Solution

3 x^{2} e^{x} + e^{x} (x^{3} + 9)

Solution steps

\frac{d}{d x} ((x^{3} + 9) e^{x})

Apply the Product Rule:

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

f = x^{3} + 9, g = e^{x}

= \frac{d}{d x} (x^{3} + 9) e^{x} + \frac{d}{d x} (e^{x}) (x^{3} + 9)

\frac{d}{d x} (x^{3} + 9) = 3 x^{2}

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

= 3 x^{2} e^{x} + e^{x} (x^{3} + 9)

Popular Examples

integral from e to e^3 of (15)/y

\int_{e}^{e^{3}} \frac{15}{y} d y

integral of x^2cos^2(x)

\int x^{2} cos^{2} (x) d x

y^{''}+8y^'-9y=0,y(1)=2,y^'(1)=0

y^{^{''}} + 8 y^{^{'}} - 9 y = 0, y (1) = 2, y^{^{'}} (1) = 0

(dy)/(dx)=(e^{2x})/(4y^3)

\frac{d y}{d x} = \frac{e ^{2 x}}{4 y ^{3}}

derivative of ln(cos^2(x+5x^3))

\frac{d}{d x} (ln (cos^{2} (x) + 5 x^{3}))

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(x^3+9)e^x ?
The derivative of f(x)=(x^3+9)e^x is 3x^2e^x+e^x(x^3+9)
What is the first derivative of f(x)=(x^3+9)e^x ?
The first derivative of f(x)=(x^3+9)e^x is 3x^2e^x+e^x(x^3+9)