What is the derivative of f(x)=8arcsin(x^3) ?

The derivative of f(x)=8arcsin(x^3) is (24x^2)/(sqrt(1-x^6))

What is the first derivative of f(x)=8arcsin(x^3) ?

The first derivative of f(x)=8arcsin(x^3) is (24x^2)/(sqrt(1-x^6))

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derivative of

f (x) = 8 arcsin (x^{3})

\frac{24 x ^{2}}{1 - x ^{6}}

Solution steps

\frac{d}{d x} (8 arcsin (x^{3}))

Take the constant out:

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

= 8 \frac{d}{d x} (arcsin (x^{3}))

Apply the chain rule:

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

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

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

= 8 \cdot \frac{1}{1 - ( x ^{3} ) ^{2}} \cdot 3 x^{2}

Simplify

8 \cdot \frac{1}{1 - ( x ^{3} ) ^{2}} \cdot 3 x^{2} : \frac{24 x ^{2}}{1 - x ^{6}}

= \frac{24 x ^{2}}{1 - x ^{6}}

f (x) = 2 x^{3} - 5 x^{4}

\int \frac{y}{e ^{y}} d y

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x^{2}, x^{2} - 4 x + 4, 0, 1

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What is the derivative of f(x)=8arcsin(x^3) ?
The derivative of f(x)=8arcsin(x^3) is (24x^2)/(sqrt(1-x^6))
What is the first derivative of f(x)=8arcsin(x^3) ?
The first derivative of f(x)=8arcsin(x^3) is (24x^2)/(sqrt(1-x^6))