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Popular >

derivative of e^x(13x^2-26x+26)

Solution

\frac{d}{d x} (e^{x} (13 x^{2} - 26 x + 26))

Solution

13 e^{x} x^{2}

Solution steps

\frac{d}{d x} (e^{x} (13 x^{2} - 26 x + 26))

Apply the Product Rule:

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

f = e^{x}, g = 13 x^{2} - 26 x + 26

= \frac{d}{d x} (e^{x}) (13 x^{2} - 26 x + 26) + \frac{d}{d x} (13 x^{2} - 26 x + 26) e^{x}

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

\frac{d}{d x} (13 x^{2} - 26 x + 26) = 26 x - 26

= e^{x} (13 x^{2} - 26 x + 26) + (26 x - 26) e^{x}

Simplify

e^{x} (13 x^{2} - 26 x + 26) + (26 x - 26) e^{x} : 13 e^{x} x^{2}

= 13 e^{x} x^{2}

Popular Examples

x^2y^{''}+xy^'+9y=0

x^{2} y^{^{''}} + x y^{^{'}} + 9 y = 0

(\partial)/(\partial x)(ysin(x/y))

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

derivative of f(x)=(x^2-6x+1)/(x^2+4)derivative of

f (x) = \frac{x ^{2} - 6 x + 1}{x ^{2} + 4}

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\int (x + 3)^{2} (2 - x)^{5} d x

y^{''}+6y+9=0,y(0)=-3,y^'(0)=-1

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Frequently Asked Questions (FAQ)

What is the derivative of e^x(13x^2-26x+26) ?
The derivative of e^x(13x^2-26x+26) is 13e^xx^2
What is the first derivative of e^x(13x^2-26x+26) ?
The first derivative of e^x(13x^2-26x+26) is 13e^xx^2