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Popular >

derivative of (9x^2-15xe^x)

Solution

\frac{d}{d 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 1/(9sin^2(x))

\int \frac{1}{9 sin ^{2} ( x )} d x

limit as x approaches 0 of (tan(4x))/(tan(9x))

x \to 0 lim (\frac{tan ( 4 x )}{tan ( 9 x )})

limit as x approaches 1 of ((x^{7a}-7ax+7a-1))/((x-1)^2)

x \to 1 lim (\frac{( x ^{7 a} - 7 a x + 7 a - 1 )}{( x - 1 ) ^{2}})

integral of 1/((x+8)^2)

\int \frac{1}{( x + 8 ) ^{2}} d x

derivative of-yln(x-(1-y)ln(1-x))

\frac{d}{d x} (- y ln (x) - (1 - y) ln (1 - x))

Frequently Asked Questions (FAQ)

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