What is the derivative of e^{x^4}*4x^3 ?

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

What is the first derivative of e^{x^4}*4x^3 ?

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = e^{x^{4}}, g = x^{3}

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

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

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

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

e^{x^{4}} \cdot 4 x^{3} x^{3} = 4 e^{x^{4}} x^{6}

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

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