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Popular >

derivative of (9x+3e^{2x^2+3})

Solution

\frac{d}{d x} ((9 x + 3) e^{2 x^{2} + 3})

Solution

9 e^{2 x^{2} + 3} + e^{2 x^{2} + 3} \cdot 4 x (9 x + 3)

Solution steps

\frac{d}{d x} ((9 x + 3) e^{2 x^{2} + 3})

Apply the Product Rule:

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

f = 9 x + 3, g = e^{2 x^{2} + 3}

= \frac{d}{d x} (9 x + 3) e^{2 x^{2} + 3} + \frac{d}{d x} (e^{2 x^{2} + 3}) (9 x + 3)

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

\frac{d}{d x} (e^{2 x^{2} + 3}) = e^{2 x^{2} + 3} \cdot 4 x

= 9 e^{2 x^{2} + 3} + e^{2 x^{2} + 3} \cdot 4 x (9 x + 3)

Popular Examples

(y-y/(x^2)e^{y/x})dx+(x+1/x e^{y/x})dy=0

(y - \frac{y}{x ^{2}} e^{\frac{y}{x}}) d x + (x + \frac{1}{x} e^{\frac{y}{x}}) d y = 0

derivative of (x^2+5x-1/(x^2))

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

derivative of-3+12x-3x^2 derivative of

- 3 + 12 x - 3 x^{2}

limit as x approaches-1 of 3x^3

x \to - 1 lim (3 x^{3})

integral of sec^3(u)

\int sec^{3} (u) d u

Frequently Asked Questions (FAQ)

What is the derivative of (9x+3e^{2x^2+3}) ?
The derivative of (9x+3e^{2x^2+3}) is 9e^{2x^2+3}+e^{2x^2+3}*4x(9x+3)
What is the first derivative of (9x+3e^{2x^2+3}) ?
The first derivative of (9x+3e^{2x^2+3}) is 9e^{2x^2+3}+e^{2x^2+3}*4x(9x+3)