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

The derivative of arcsin(5x^3) is (15x^2)/(sqrt(1-25x^6))

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

The first derivative of arcsin(5x^3) is (15x^2)/(sqrt(1-25x^6))

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

\frac{15 x ^{2}}{1 - 25 x ^{6}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (5 x^{3}) = 15 x^{2}

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

Simplify

\frac{1}{1 - ( 5 x ^{3} ) ^{2}} \cdot 15 x^{2} : \frac{15 x ^{2}}{1 - 25 x ^{6}}

= \frac{15 x ^{2}}{1 - 25 x ^{6}}

\frac{d}{d x} (ln ∣ csc (3 x) ∣)

\int 4 e^{- 0.4 x} d x

\frac{∣ x ∣}{5 - x ^{2}}

\frac{d}{d x} (6 - e^{- x})

What is the derivative of arcsin(5x^3) ?
The derivative of arcsin(5x^3) is (15x^2)/(sqrt(1-25x^6))
What is the first derivative of arcsin(5x^3) ?
The first derivative of arcsin(5x^3) is (15x^2)/(sqrt(1-25x^6))