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Popular >

derivative of e^x(x^2+5x)

Solution

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

Solution

e^{x} x^{2} + 7 e^{x} x + 5 e^{x}

Solution steps

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

Apply the Product Rule:

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

f = e^{x}, g = x^{2} + 5 x

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

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

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

= e^{x} (x^{2} + 5 x) + (2 x + 5) e^{x}

Simplify

e^{x} (x^{2} + 5 x) + (2 x + 5) e^{x} : e^{x} x^{2} + 7 e^{x} x + 5 e^{x}

= e^{x} x^{2} + 7 e^{x} x + 5 e^{x}

Graph

Popular Examples

derivative of xsqrt(3x-2)

\frac{d}{d x} (x 3 x - 2)

xy^'+y=0,y(4)=6

x y^{^{'}} + y = 0, y (4) = 6

derivative of f(x)= 4/x-2/(x^3)+1/(x^4)derivative of

f (x) = \frac{4}{x} - \frac{2}{x ^{3}} + \frac{1}{x ^{4}}

tangent of y=-7/2 x^2+5x+5,(-1,-7/2)tangent of

y = - \frac{7}{2} x^{2} + 5 x + 5, (- 1, - \frac{7}{2})

integral of cos^3(x)sin^{-4}(x)

\int cos^{3} (x) sin^{- 4} (x) d x

Frequently Asked Questions (FAQ)

What is the derivative of e^x(x^2+5x) ?
The derivative of e^x(x^2+5x) is e^xx^2+7e^xx+5e^x
What is the first derivative of e^x(x^2+5x) ?
The first derivative of e^x(x^2+5x) is e^xx^2+7e^xx+5e^x