What is the derivative of x^3e^{6x^3+8x^2-7} ?

The derivative of x^3e^{6x^3+8x^2-7} is 3x^2e^{6x^3+8x^2-7}+e^{6x^3+8x^2-7}(18x^2+16x)x^3

What is the first derivative of x^3e^{6x^3+8x^2-7} ?

The first derivative of x^3e^{6x^3+8x^2-7} is 3x^2e^{6x^3+8x^2-7}+e^{6x^3+8x^2-7}(18x^2+16x)x^3

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derivative of

x^{3} e^{6 x^{3} + 8 x^{2} - 7}

3 x^{2} e^{6 x^{3} + 8 x^{2} - 7} + e^{6 x^{3} + 8 x^{2} - 7} (18 x^{2} + 16 x) x^{3}

Solution steps

\frac{d}{d x} (x^{3} e^{6 x^{3} + 8 x^{2} - 7})

Apply the Product Rule:

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

f = x^{3}, g = e^{6 x^{3} + 8 x^{2} - 7}

= \frac{d}{d x} (x^{3}) e^{6 x^{3} + 8 x^{2} - 7} + \frac{d}{d x} (e^{6 x^{3} + 8 x^{2} - 7}) x^{3}

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

\frac{d}{d x} (e^{6 x^{3} + 8 x^{2} - 7}) = e^{6 x^{3} + 8 x^{2} - 7} (18 x^{2} + 16 x)

= 3 x^{2} e^{6 x^{3} + 8 x^{2} - 7} + e^{6 x^{3} + 8 x^{2} - 7} (18 x^{2} + 16 x) x^{3}

\frac{d}{d x} (arcsin (x^{3}))

f (x) = \frac{f ( x )}{x ^{2} + 2}

\int_{1}^{16} \frac{4}{x} d x

x \to 0 lim (\frac{2 x}{x ^{2} - 5 x})

\frac{\partial}{\partial x} (4 x ln (x) y)

What is the derivative of x^3e^{6x^3+8x^2-7} ?
The derivative of x^3e^{6x^3+8x^2-7} is 3x^2e^{6x^3+8x^2-7}+e^{6x^3+8x^2-7}(18x^2+16x)x^3
What is the first derivative of x^3e^{6x^3+8x^2-7} ?
The first derivative of x^3e^{6x^3+8x^2-7} is 3x^2e^{6x^3+8x^2-7}+e^{6x^3+8x^2-7}(18x^2+16x)x^3