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Popular Calculus >

derivative of (4x^2-5x)e^x

Solution

derivative of

(4 x^{2} - 5 x) e^{x}

Solution

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

Solution steps

\frac{d}{d x} ((4 x^{2} - 5 x) e^{x})

Apply the Product Rule:

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

f = 4 x^{2} - 5 x, g = e^{x}

= \frac{d}{d x} (4 x^{2} - 5 x) e^{x} + \frac{d}{d x} (e^{x}) (4 x^{2} - 5 x)

\frac{d}{d x} (4 x^{2} - 5 x) = 8 x - 5

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

= (8 x - 5) e^{x} + e^{x} (4 x^{2} - 5 x)

Simplify

(8 x - 5) e^{x} + e^{x} (4 x^{2} - 5 x) : 4 e^{x} x^{2} + 3 e^{x} x - 5 e^{x}

= 4 e^{x} x^{2} + 3 e^{x} x - 5 e^{x}

Graph

Popular Examples

area 7-x^2,x^2-1

a re a 7 - x^{2}, x^{2} - 1

derivative of (sin(pi/2 x)/x)

\frac{d}{d x} (\frac{sin ( \frac{π}{2} x )}{x})

derivative of xsqrt(x^2+y^2)

\frac{d}{d x} (x x^{2} + y^{2})

integral from 0 to 1/5 of 5arcsin(5y)

\int_{0}^{\frac{1}{5}} 5 arcsin (5 y) d y

f (x) = cos (5 x)

Frequently Asked Questions (FAQ)

What is the derivative of (4x^2-5x)e^x ?
The derivative of (4x^2-5x)e^x is 4e^xx^2+3e^xx-5e^x
What is the first derivative of (4x^2-5x)e^x ?
The first derivative of (4x^2-5x)e^x is 4e^xx^2+3e^xx-5e^x