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Popular >

derivative of (3x^2-5xe^x)

Solution

\frac{d}{d x} ((3 x^{2} - 5 x) e^{x})

Solution

3 e^{x} x^{2} + e^{x} x - 5 e^{x}

Solution steps

\frac{d}{d x} ((3 x^{2} - 5 x) e^{x})

Apply the Product Rule:

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

f = 3 x^{2} - 5 x, g = e^{x}

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

\frac{d}{d x} (3 x^{2} - 5 x) = 6 x - 5

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

= (6 x - 5) e^{x} + e^{x} (3 x^{2} - 5 x)

Simplify

(6 x - 5) e^{x} + e^{x} (3 x^{2} - 5 x) : 3 e^{x} x^{2} + e^{x} x - 5 e^{x}

= 3 e^{x} x^{2} + e^{x} x - 5 e^{x}

Graph

Popular Examples

integral of e^{5x}cos(6x)

\int e^{5 x} cos (6 x) d x

derivative of (ln(x^2)^{-3})

\frac{d}{d x} ((ln (x^{2}))^{- 3})

derivative of (arctan(x)^2)

\frac{d}{d x} ((arctan (x))^{2})

derivative of 2sin(pix+3cos(pi)x)

\frac{d}{d x} (2 sin (π) x + 3 cos (π) x)

domain of f(x)= 7/(1-x)domain

f (x) = \frac{7}{1 - x}

Frequently Asked Questions (FAQ)

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