What is the derivative of 6x^2*e^{(x^3)/3} ?

The derivative of 6x^2*e^{(x^3)/3} is 6(2e^{(x^3)/3}x+e^{(x^3)/3}x^4)

What is the first derivative of 6x^2*e^{(x^3)/3} ?

The first derivative of 6x^2*e^{(x^3)/3} is 6(2e^{(x^3)/3}x+e^{(x^3)/3}x^4)

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derivative of

6 x^{2} \cdot e^{\frac{x ^{3}}{3}}

6 (2 e^{\frac{x ^{3}}{3}} x + e^{\frac{x ^{3}}{3}} x^{4})

Solution steps

\frac{d}{d x} (6 x^{2} e^{\frac{x ^{3}}{3}})

Take the constant out:

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

= 6 \frac{d}{d x} (x^{2} e^{\frac{x ^{3}}{3}})

Apply the Product Rule:

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

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

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

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

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

= 6 (2 x e^{\frac{x ^{3}}{3}} + e^{\frac{x ^{3}}{3}} x^{2} x^{2})

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

= 6 (2 e^{\frac{x ^{3}}{3}} x + e^{\frac{x ^{3}}{3}} x^{4})

8 x + 9 x

(1 + t)^{7}

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

\int_{1}^{6} x^{3} ln (4 x) d x

\frac{( s + 1 )}{( s + 2 ) ^{2}}

What is the derivative of 6x^2*e^{(x^3)/3} ?
The derivative of 6x^2*e^{(x^3)/3} is 6(2e^{(x^3)/3}x+e^{(x^3)/3}x^4)
What is the first derivative of 6x^2*e^{(x^3)/3} ?
The first derivative of 6x^2*e^{(x^3)/3} is 6(2e^{(x^3)/3}x+e^{(x^3)/3}x^4)