What is the derivative of (x^3+5)e^x ?

The derivative of (x^3+5)e^x is 3x^2e^x+e^x(x^3+5)

What is the first derivative of (x^3+5)e^x ?

The first derivative of (x^3+5)e^x is 3x^2e^x+e^x(x^3+5)

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derivative of

(x^{3} + 5) e^{x}

3 x^{2} e^{x} + e^{x} (x^{3} + 5)

Solution steps

\frac{d}{d x} ((x^{3} + 5) e^{x})

Apply the Product Rule:

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

f = x^{3} + 5, g = e^{x}

= \frac{d}{d x} (x^{3} + 5) e^{x} + \frac{d}{d x} (e^{x}) (x^{3} + 5)

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

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

= 3 x^{2} e^{x} + e^{x} (x^{3} + 5)

\frac{d}{d x} (in y (x))

\int_{1}^{10} \frac{1}{x ^{2} - 4 x - 32} d x

g (x) = \frac{1}{5 x ^{2} + 4 x}

\frac{ln ( x )}{3 x}, \frac{( ln ( x ) ) ^{2}}{3 x}

y^{^{'}} - \frac{3}{x} y = \frac{y ^{5}}{x ^{6}}

What is the derivative of (x^3+5)e^x ?
The derivative of (x^3+5)e^x is 3x^2e^x+e^x(x^3+5)
What is the first derivative of (x^3+5)e^x ?
The first derivative of (x^3+5)e^x is 3x^2e^x+e^x(x^3+5)