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

The derivative of f(x)=4arcsin(x^4) is (16x^3)/(sqrt(1-x^8))

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

The first derivative of f(x)=4arcsin(x^4) is (16x^3)/(sqrt(1-x^8))

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derivative of

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

\frac{16 x ^{3}}{1 - x ^{8}}

Solution steps

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

Take the constant out:

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

= 4 \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}

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

Simplify

4 \cdot \frac{1}{1 - ( x ^{4} ) ^{2}} \cdot 4 x^{3} : \frac{16 x ^{3}}{1 - x ^{8}}

= \frac{16 x ^{3}}{1 - x ^{8}}

\frac{d}{d x} (- x^{5} - \frac{x ^{3}}{6} + \frac{3}{x} - \frac{1}{x ^{2}})

y = \frac{7}{( 6 x ) ^{6}}

4 x, 64 - x^{2}, [0, 6.928]

x \to 69.9 lim (\frac{ln ( \frac{x - 70}{230} )}{- 0.19})

y = x^{2} - 12, y = 11 x

What is the derivative of f(x)=4arcsin(x^4) ?
The derivative of f(x)=4arcsin(x^4) is (16x^3)/(sqrt(1-x^8))
What is the first derivative of f(x)=4arcsin(x^4) ?
The first derivative of f(x)=4arcsin(x^4) is (16x^3)/(sqrt(1-x^8))