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Popular >

derivative of e^{5x}+5e^{5x}x

Solution

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

Solution

25 e^{5 x} x + 10 e^{5 x}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= e^{5 x} \cdot 5 + 5 (5 e^{5 x} x + e^{5 x})

Simplify

e^{5 x} \cdot 5 + 5 (5 e^{5 x} x + e^{5 x}) : 25 e^{5 x} x + 10 e^{5 x}

= 25 e^{5 x} x + 10 e^{5 x}

Popular Examples

derivative of sqrt(x^2+4xy+y^6)-8

\frac{d}{d x} (x^{2} + 4 x y + y^{6} - 8)

integral from 3 to 4 of 9x

\int_{3}^{4} 9 x d x

integral of (3x^2-4x+5)/((x-1)(x^2+1))

\int \frac{3 x ^{2} - 4 x + 5}{( x - 1 ) ( x ^{2} + 1 )} d x

derivative of (sin(2x)^x)

\frac{d}{d x} ((sin (2 x))^{x})

integral of 3(5^{1-2x})

\int 3 (5^{1 - 2 x}) d x

Frequently Asked Questions (FAQ)

What is the derivative of e^{5x}+5e^{5x}x ?
The derivative of e^{5x}+5e^{5x}x is 25e^{5x}x+10e^{5x}
What is the first derivative of e^{5x}+5e^{5x}x ?
The first derivative of e^{5x}+5e^{5x}x is 25e^{5x}x+10e^{5x}