What is the derivative of (2-sqrt(x)^4) ?

The derivative of (2-sqrt(x)^4) is -(2(-sqrt(x)+2)^3)/(sqrt(x))

What is the first derivative of (2-sqrt(x)^4) ?

The first derivative of (2-sqrt(x)^4) is -(2(-sqrt(x)+2)^3)/(sqrt(x))

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

- \frac{2 ( - x + 2 ) ^{3}}{x}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (2 - x) = - \frac{1}{2 x}

= 4 (2 - x)^{3} (- \frac{1}{2 x})

Simplify

4 (2 - x)^{3} (- \frac{1}{2 x}) : - \frac{2 ( - x + 2 ) ^{3}}{x}

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

(u - u) (u + u)

y^{^{'}} + 2 y = e^{- x}

\int 2 x \cdot cos (x^{2}) d x

x y^{^{'}} = 2 x + 3 y

n = 2 \sum \infty (- 1)^{n}

What is the derivative of (2-sqrt(x)^4) ?
The derivative of (2-sqrt(x)^4) is -(2(-sqrt(x)+2)^3)/(sqrt(x))
What is the first derivative of (2-sqrt(x)^4) ?
The first derivative of (2-sqrt(x)^4) is -(2(-sqrt(x)+2)^3)/(sqrt(x))