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Popular >

derivative of 10x^{10}e^x

Solution

\frac{d}{d x} (10 x^{10} e^{x})

Solution

10 (10 x^{9} e^{x} + e^{x} x^{10})

Solution steps

\frac{d}{d x} (10 x^{10} e^{x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 10 \frac{d}{d x} (x^{10} e^{x})

Apply the Product Rule:

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

f = x^{10}, g = e^{x}

= 10 (\frac{d}{d x} (x^{10}) e^{x} + \frac{d}{d x} (e^{x}) x^{10})

\frac{d}{d x} (x^{10}) = 10 x^{9}

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

= 10 (10 x^{9} e^{x} + e^{x} x^{10})

Popular Examples

integral of 1/(sqrt(-t^2+8t-15))

\int \frac{1}{- t ^{2} + 8 t - 15} d t

derivative of x+e^x-1/x derivative of

x + e^{x} - \frac{1}{x}

integral of ((4x-5))/((x-2)(x+3))

\int \frac{( 4 x - 5 )}{( x - 2 ) ( x + 3 )} d x

integral of y/(x(x+y))

\int \frac{y}{x ( x + y )} d x

xy^'+y=e^x,y(1)=6

x y^{^{'}} + y = e^{x}, y (1) = 6

Frequently Asked Questions (FAQ)

What is the derivative of 10x^{10}e^x ?
The derivative of 10x^{10}e^x is 10(10x^9e^x+e^xx^{10})
What is the first derivative of 10x^{10}e^x ?
The first derivative of 10x^{10}e^x is 10(10x^9e^x+e^xx^{10})