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Popular >

derivative of 9e^{3x}x+6e^{3x}

Solution

\frac{d}{d x} (9 e^{3 x} x + 6 e^{3 x})

Solution

27 e^{3 x} x + 27 e^{3 x}

Solution steps

\frac{d}{d x} (9 e^{3 x} x + 6 e^{3 x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (9 e^{3 x} x) + \frac{d}{d x} (6 e^{3 x})

\frac{d}{d x} (9 e^{3 x} x) = 9 (3 e^{3 x} x + e^{3 x})

\frac{d}{d x} (6 e^{3 x}) = 18 e^{3 x}

= 9 (3 e^{3 x} x + e^{3 x}) + 18 e^{3 x}

Simplify

9 (3 e^{3 x} x + e^{3 x}) + 18 e^{3 x} : 27 e^{3 x} x + 27 e^{3 x}

= 27 e^{3 x} x + 27 e^{3 x}

Popular Examples

integral of (6x^2-4x+5)

\int (6 x^{2} - 4 x + 5) d x

integral of 1/(x^3+9x)

\int \frac{1}{x ^{3} + 9 x} d x

tangent of 5sec(x),\at x= pi/3 tangent of

5 sec (x), at x = \frac{π}{3}

area-x^2+3x,2x^3-x^2-5x area

- x^{2} + 3 x, 2 x^{3} - x^{2} - 5 x

limit as x approaches 0 of ((x-1))/x

x \to 0 lim (\frac{( x - 1 )}{x})

Frequently Asked Questions (FAQ)

What is the derivative of 9e^{3x}x+6e^{3x} ?
The derivative of 9e^{3x}x+6e^{3x} is 27e^{3x}x+27e^{3x}
What is the first derivative of 9e^{3x}x+6e^{3x} ?
The first derivative of 9e^{3x}x+6e^{3x} is 27e^{3x}x+27e^{3x}