What is the derivative of f(x)=5arcsin(x^3) ?

The derivative of f(x)=5arcsin(x^3) is (15x^2)/(sqrt(1-x^6))

What is the first derivative of f(x)=5arcsin(x^3) ?

The first derivative of f(x)=5arcsin(x^3) is (15x^2)/(sqrt(1-x^6))

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derivative of

f (x) = 5 arcsin (x^{3})

\frac{15 x ^{2}}{1 - x ^{6}}

Solution steps

\frac{d}{d x} (5 arcsin (x^{3}))

Take the constant out:

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

= 5 \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}

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

Simplify

5 \cdot \frac{1}{1 - ( x ^{3} ) ^{2}} \cdot 3 x^{2} : \frac{15 x ^{2}}{1 - x ^{6}}

= \frac{15 x ^{2}}{1 - x ^{6}}

\frac{e ^{x}}{x}

\int_{1}^{2} x ln (x) d x

x \frac{d y}{d x} + (2 x + 1) y = x e^{- 2 x}

\int \frac{x ^{2}}{x - 2} d x

\int (e^{x} + 1)^{3} e^{x} d x

What is the derivative of f(x)=5arcsin(x^3) ?
The derivative of f(x)=5arcsin(x^3) is (15x^2)/(sqrt(1-x^6))
What is the first derivative of f(x)=5arcsin(x^3) ?
The first derivative of f(x)=5arcsin(x^3) is (15x^2)/(sqrt(1-x^6))