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Popular >

derivative of f(x)=e^{9x}+9e^{9x}x

Solution

derivative of

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

Solution

81 e^{9 x} x + 18 e^{9 x}

Solution steps

\frac{d}{d x} (e^{9 x} + 9 e^{9 x} x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (e^{9 x}) + \frac{d}{d x} (9 e^{9 x} x)

\frac{d}{d x} (e^{9 x}) = e^{9 x} \cdot 9

\frac{d}{d x} (9 e^{9 x} x) = 9 (9 e^{9 x} x + e^{9 x})

= e^{9 x} \cdot 9 + 9 (9 e^{9 x} x + e^{9 x})

Simplify

e^{9 x} \cdot 9 + 9 (9 e^{9 x} x + e^{9 x}) : 81 e^{9 x} x + 18 e^{9 x}

= 81 e^{9 x} x + 18 e^{9 x}

Popular Examples

derivative of x^3+xe^y-2y

\frac{d}{d x} (x^{3} + x e^{y} - 2 y)

integral of 1/((x^2+4)^2)

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

integral of 6x(-x^2+5)^7

\int 6 x (- x^{2} + 5)^{7} d x

x^2-3xy+x(dy)/(dx)=0

x^{2} - 3 x y + x \frac{d y}{d x} = 0

limit as x approaches 2 of (2-x)/(x-2)

x \to 2 lim (\frac{2 - x}{x - 2})

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=e^{9x}+9e^{9x}x ?
The derivative of f(x)=e^{9x}+9e^{9x}x is 81e^{9x}x+18e^{9x}
What is the first derivative of f(x)=e^{9x}+9e^{9x}x ?
The first derivative of f(x)=e^{9x}+9e^{9x}x is 81e^{9x}x+18e^{9x}