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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= e^{3 x} \cdot 3 + 3 (3 e^{3 x} x + e^{3 x})

Simplify

e^{3 x} \cdot 3 + 3 (3 e^{3 x} x + e^{3 x}) : 9 e^{3 x} x + 6 e^{3 x}

= 9 e^{3 x} x + 6 e^{3 x}

Graph

Popular Examples

limit as x approaches 0 of-6x+9

x \to 0 lim (- 6 x + 9)

integral from 1 to 4 of (x^2-4x+2)

\int_{1}^{4} (x^{2} - 4 x + 2) d x

derivative of y=12xsin(x)derivative of

y = 12 x sin (x)

9x^2(dy)/(dx)=(dy)/(dx)+2xe^{-y}

9 x^{2} \frac{d y}{d x} = \frac{d y}{d x} + 2 x e^{- y}

laplacetransform t^4 laplace transform

t^{4}

Frequently Asked Questions (FAQ)

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