What is the derivative of f(x)=2000(x^2+5)^{1/3} ?

The derivative of f(x)=2000(x^2+5)^{1/3} is (4000x)/(3(x^2+5)^{2/3)}

What is the first derivative of f(x)=2000(x^2+5)^{1/3} ?

The first derivative of f(x)=2000(x^2+5)^{1/3} is (4000x)/(3(x^2+5)^{2/3)}

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derivative of

f (x) = 2000 (x^{2} + 5)^{\frac{1}{3}}

\frac{4000 x}{3 ( x ^{2} + 5 ) ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} (2000 (x^{2} + 5)^{\frac{1}{3}})

Take the constant out:

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

= 2000 \frac{d}{d x} ((x^{2} + 5)^{\frac{1}{3}})

Apply the chain rule:

\frac{1}{3 ( x ^{2} + 5 ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{2} + 5)

= \frac{1}{3 ( x ^{2} + 5 ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{2} + 5)

\frac{d}{d x} (x^{2} + 5) = 2 x

= 2000 \cdot \frac{1}{3 ( x ^{2} + 5 ) ^{\frac{2}{3}}} \cdot 2 x

Simplify

2000 \cdot \frac{1}{3 ( x ^{2} + 5 ) ^{\frac{2}{3}}} \cdot 2 x : \frac{4000 x}{3 ( x ^{2} + 5 ) ^{\frac{2}{3}}}

= \frac{4000 x}{3 ( x ^{2} + 5 ) ^{\frac{2}{3}}}

\int_{0}^{2} e^{- x^{2}} d x

\frac{\partial}{\partial x} (x^{0.5} + y)

\frac{d}{d x} (4 x^{3} - 10 x^{2})

(4 x^{2})^{^{'}}

\frac{\partial}{\partial x} (e^{- (x - y)^{2}})

What is the derivative of f(x)=2000(x^2+5)^{1/3} ?
The derivative of f(x)=2000(x^2+5)^{1/3} is (4000x)/(3(x^2+5)^{2/3)}
What is the first derivative of f(x)=2000(x^2+5)^{1/3} ?
The first derivative of f(x)=2000(x^2+5)^{1/3} is (4000x)/(3(x^2+5)^{2/3)}