What is the derivative of f(x)=5arcsin(x^4) ?

The derivative of f(x)=5arcsin(x^4) is (20x^3)/(sqrt(1-x^8))

What is the first derivative of f(x)=5arcsin(x^4) ?

The first derivative of f(x)=5arcsin(x^4) is (20x^3)/(sqrt(1-x^8))

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derivative of

f (x) = 5 arcsin (x^{4})

\frac{20 x ^{3}}{1 - x ^{8}}

Solution steps

\frac{d}{d x} (5 arcsin (x^{4}))

Take the constant out:

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

= 5 \frac{d}{d x} (arcsin (x^{4}))

Apply the chain rule:

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

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

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

= 5 \cdot \frac{1}{1 - ( x ^{4} ) ^{2}} \cdot 4 x^{3}

Simplify

5 \cdot \frac{1}{1 - ( x ^{4} ) ^{2}} \cdot 4 x^{3} : \frac{20 x ^{3}}{1 - x ^{8}}

= \frac{20 x ^{3}}{1 - x ^{8}}

What is the derivative of f(x)=5arcsin(x^4) ?
The derivative of f(x)=5arcsin(x^4) is (20x^3)/(sqrt(1-x^8))
What is the first derivative of f(x)=5arcsin(x^4) ?
The first derivative of f(x)=5arcsin(x^4) is (20x^3)/(sqrt(1-x^8))