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Popular >

derivative of f(x)=(9x^2-15x)e^x

Solution

derivative of

f (x) = (9 x^{2} - 15 x) e^{x}

Solution

9 e^{x} x^{2} + 3 e^{x} x - 15 e^{x}

Solution steps

\frac{d}{d x} ((9 x^{2} - 15 x) e^{x})

Apply the Product Rule:

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

f = 9 x^{2} - 15 x, g = e^{x}

= \frac{d}{d x} (9 x^{2} - 15 x) e^{x} + \frac{d}{d x} (e^{x}) (9 x^{2} - 15 x)

\frac{d}{d x} (9 x^{2} - 15 x) = 18 x - 15

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

= (18 x - 15) e^{x} + e^{x} (9 x^{2} - 15 x)

Simplify

(18 x - 15) e^{x} + e^{x} (9 x^{2} - 15 x) : 9 e^{x} x^{2} + 3 e^{x} x - 15 e^{x}

= 9 e^{x} x^{2} + 3 e^{x} x - 15 e^{x}

Popular Examples

integral of sin(x)cos(x)ln(sin(x))

\int sin (x) cos (x) ln (sin (x)) d x

y^{''}-3y^'+2y=0,y(0)=1,y^'(0)=-7/3

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (0) = 1, y^{^{'}} (0) = - \frac{7}{3}

integral from 0 to 1 of sqrt(4-x^2)

\int_{0}^{1} 4 - x^{2} d x

integral of 9/(x^4)

\int \frac{9}{x ^{4}} d x

tangent of y=(sqrt(x))/(x+1),(4, 2/5)tangent of

y = \frac{x}{x + 1}, (4, \frac{2}{5})

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(9x^2-15x)e^x ?
The derivative of f(x)=(9x^2-15x)e^x is 9e^xx^2+3e^xx-15e^x
What is the first derivative of f(x)=(9x^2-15x)e^x ?
The first derivative of f(x)=(9x^2-15x)e^x is 9e^xx^2+3e^xx-15e^x