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

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

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

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

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derivative of

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}}

\frac{d}{d x} (- 131072 sin (2 x))

x \to (- 1^{+}) lim (4 x^{3} - 2 m)

ln (3 x^{3} + 2)

\frac{\partial}{\partial r} (2 t + r^{2} cos (t))

\int \frac{e ^{4 x}}{1 + e ^{2 x}} d x

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