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Popular >

derivative of (x-9)e^x

Solution

derivative of

(x - 9) e^{x}

Solution

e^{x} x - 8 e^{x}

Solution steps

\frac{d}{d x} ((x - 9) e^{x})

Apply the Product Rule:

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

f = x - 9, g = e^{x}

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

\frac{d}{d x} (x - 9) = 1

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

= 1 \cdot e^{x} + e^{x} (x - 9)

Simplify

1 \cdot e^{x} + e^{x} (x - 9) : e^{x} x - 8 e^{x}

= e^{x} x - 8 e^{x}

Graph

Popular Examples

integral of (sin^3(x))/(1-cos^2(x))

\int \frac{sin ^{3} ( x )}{1 - cos ^{2} ( x )} d x

integral of u^{1/3}

\int u^{\frac{1}{3}} d u

(\partial)/(\partial x)(sin(x)-cos(xy))

\frac{\partial}{\partial x} (sin (x) - cos (x y))

(\partial)/(\partial x)(63x^3cos(9x^2y))

\frac{\partial}{\partial x} (63 x^{3} cos (9 x^{2} y))

f (x) = - 8 cos (2 x)

Frequently Asked Questions (FAQ)

What is the derivative of (x-9)e^x ?
The derivative of (x-9)e^x is e^xx-8e^x
What is the first derivative of (x-9)e^x ?
The first derivative of (x-9)e^x is e^xx-8e^x