What is the derivative of sqrt((x+2^2*(x^2)/2)) ?

The derivative of sqrt((x+2^2*(x^2)/2)) is sqrt(2)(x+1)

What is the first derivative of sqrt((x+2^2*(x^2)/2)) ?

The first derivative of sqrt((x+2^2*(x^2)/2)) is sqrt(2)(x+1)

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

2 (x + 1)

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{2 ( x + 2 ) ^{2} \frac{x ^{2}}{2}} \cdot 2 x (x + 2) (x + 1)

Simplify

\frac{1}{2 ( x + 2 ) ^{2} \frac{x ^{2}}{2}} \cdot 2 x (x + 2) (x + 1) : 2 (x + 1)

= 2 (x + 1)

\frac{d}{d x} (\frac{e ^{x}}{5 x ^{3}})

f (x) = (1 + 5 x)^{12}, (0, 1)

10 y^{^{'}} = 10 \cdot 9.81 - 5 y

y = \frac{1}{x - 1}, at x = 6

y^{^{''}} - 4 y^{^{'}} + 3 y = 0

What is the derivative of sqrt((x+2^2*(x^2)/2)) ?
The derivative of sqrt((x+2^2*(x^2)/2)) is sqrt(2)(x+1)
What is the first derivative of sqrt((x+2^2*(x^2)/2)) ?
The first derivative of sqrt((x+2^2*(x^2)/2)) is sqrt(2)(x+1)