What is the derivative of f(x)=3arcsin(x^4) ?

The derivative of f(x)=3arcsin(x^4) is (12x^3)/(sqrt(1-x^8))

What is the first derivative of f(x)=3arcsin(x^4) ?

The first derivative of f(x)=3arcsin(x^4) is (12x^3)/(sqrt(1-x^8))

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derivative of

f (x) = 3 arcsin (x^{4})

\frac{12 x ^{3}}{1 - x ^{8}}

Solution steps

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

Take the constant out:

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

= 3 \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}

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

Simplify

3 \cdot \frac{1}{1 - ( x ^{4} ) ^{2}} \cdot 4 x^{3} : \frac{12 x ^{3}}{1 - x ^{8}}

= \frac{12 x ^{3}}{1 - x ^{8}}

\int_{0}^{1} 3 x^{2} d x

x \to - 2 lim (\frac{4 - x ^{2}}{x + 2})

\int 10 sinh (4 x - ln (2)) d x

\int ln (x) x d x

\frac{d}{d x} ((x ln (x))^{2})

What is the derivative of f(x)=3arcsin(x^4) ?
The derivative of f(x)=3arcsin(x^4) is (12x^3)/(sqrt(1-x^8))
What is the first derivative of f(x)=3arcsin(x^4) ?
The first derivative of f(x)=3arcsin(x^4) is (12x^3)/(sqrt(1-x^8))