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Popular >

derivative of (8x^2-16x+16e^x)

Solution

\frac{d}{d x} ((8 x^{2} - 16 x + 16) e^{x})

Solution

8 e^{x} x^{2}

Solution steps

\frac{d}{d x} ((8 x^{2} - 16 x + 16) e^{x})

Apply the Product Rule:

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

f = 8 x^{2} - 16 x + 16, g = e^{x}

= \frac{d}{d x} (8 x^{2} - 16 x + 16) e^{x} + \frac{d}{d x} (e^{x}) (8 x^{2} - 16 x + 16)

\frac{d}{d x} (8 x^{2} - 16 x + 16) = 16 x - 16

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

= (16 x - 16) e^{x} + e^{x} (8 x^{2} - 16 x + 16)

Simplify

(16 x - 16) e^{x} + e^{x} (8 x^{2} - 16 x + 16) : 8 e^{x} x^{2}

= 8 e^{x} x^{2}

Popular Examples

integral of (20x^3-40x^2+9)/(x^2-2x)

\int \frac{20 x ^{3} - 40 x ^{2} + 9}{x ^{2} - 2 x} d x

(\partial)/(\partial x)((2x+1)^2)

\frac{\partial}{\partial x} ((2 x + 1)^{2})

derivative of 4x^2

\frac{d}{d x} (4 x^{2})

(\partial)/(\partial z)(e^x)

\frac{\partial}{\partial z} (e^{x})

derivative of x^25e^x

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

Frequently Asked Questions (FAQ)

What is the derivative of (8x^2-16x+16e^x) ?
The derivative of (8x^2-16x+16e^x) is 8e^xx^2
What is the first derivative of (8x^2-16x+16e^x) ?
The first derivative of (8x^2-16x+16e^x) is 8e^xx^2