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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

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

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

t^{2} y^{^{'}} + 2 t y = 3

\int \frac{3}{x ( x ^{2} + 25 )} d x

6 x^{3} + \frac{7}{x}

(4 x^{2}) y^{^{''}} + 4 x y^{^{'}} = 0

y^{^{''}} + 3 y^{^{'}} = 5

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