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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

y^{^{''}} - 8 y^{^{'}} + 18 y = 0, y (0) = 1, y^{^{'}} (0) = - 4

\int (8 x^{2} + 5)^{10} x d x

\int 2 x (x^{2} + 7)^{7} d x

\frac{d y}{d x} = - \frac{1}{3} x^{3}

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

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