What is the derivative of e^{x^3}*3x^2 ?

The derivative of e^{x^3}*3x^2 is 3(3e^{x^3}x^4+2e^{x^3}x)

What is the first derivative of e^{x^3}*3x^2 ?

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

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

3 (3 e^{x^{3}} x^{4} + 2 e^{x^{3}} x)

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

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

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

e^{x^{3}} \cdot 3 x^{2} x^{2} = 3 e^{x^{3}} x^{4}

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

\frac{d}{d x} (2 x^{3} e^{- 0.6 x})

\int \frac{v}{v ^{2} + 1} d v

\int \frac{x ^{2} + 6}{x ^{3} + x ^{2} - 2 x} d x

f (x) = \frac{2}{x + 7}, (- 8, - 2)

\frac{d}{d x} (e^{x} arctan (x))

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