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

The derivative of (e^{(x^2}+4)^2(4x)^3x) is 64(4x^3(e^{x^2}+4)^2+4e^{x^2}x^5(e^{x^2}+4))

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

The first derivative of (e^{(x^2}+4)^2(4x)^3x) is 64(4x^3(e^{x^2}+4)^2+4e^{x^2}x^5(e^{x^2}+4))

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

64 (4 x^{3} (e^{x^{2}} + 4)^{2} + 4 e^{x^{2}} x^{5} (e^{x^{2}} + 4))

Solution steps

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

Simplify

(e^{(x^{2})} + 4)^{2} (4 x)^{3} x : 64 x^{4} (e^{x^{2}} + 4)^{2}

= \frac{d}{d x} (64 x^{4} (e^{x^{2}} + 4)^{2})

Take the constant out:

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

= 64 \frac{d}{d x} (x^{4} (e^{x^{2}} + 4)^{2})

Apply the Product Rule:

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

f = x^{4}, g = (e^{x^{2}} + 4)^{2}

= 64 (\frac{d}{d x} (x^{4}) (e^{x^{2}} + 4)^{2} + \frac{d}{d x} ((e^{x^{2}} + 4)^{2}) x^{4})

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

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

= 64 (4 x^{3} (e^{x^{2}} + 4)^{2} + 4 e^{x^{2}} x (e^{x^{2}} + 4) x^{4})

4 e^{x^{2}} x (e^{x^{2}} + 4) x^{4} = 4 e^{x^{2}} x^{5} (e^{x^{2}} + 4)

= 64 (4 x^{3} (e^{x^{2}} + 4)^{2} + 4 e^{x^{2}} x^{5} (e^{x^{2}} + 4))

\int \frac{1}{sin ( x ) cos ^{3} ( x )} d x

\int_{3}^{4} \frac{( 2 x - 3 )}{6} d x

1 - 9 x^{2} y^{^{'}} = x

\frac{d}{d x} (\frac{∣ x ∣}{2 - x ^{2}})

\frac{d y}{d t} + 5 y = 5

What is the derivative of (e^{(x^2}+4)^2(4x)^3x) ?
The derivative of (e^{(x^2}+4)^2(4x)^3x) is 64(4x^3(e^{x^2}+4)^2+4e^{x^2}x^5(e^{x^2}+4))
What is the first derivative of (e^{(x^2}+4)^2(4x)^3x) ?
The first derivative of (e^{(x^2}+4)^2(4x)^3x) is 64(4x^3(e^{x^2}+4)^2+4e^{x^2}x^5(e^{x^2}+4))