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Popular >

derivative of 6arcsin(x^3)

Solution

\frac{d}{d x} (6 arcsin (x^{3}))

Solution

\frac{18 x ^{2}}{1 - x ^{6}}

Solution steps

\frac{d}{d x} (6 arcsin (x^{3}))

Take the constant out:

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

= 6 \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}

= 6 \cdot \frac{1}{1 - ( x ^{3} ) ^{2}} \cdot 3 x^{2}

Simplify

6 \cdot \frac{1}{1 - ( x ^{3} ) ^{2}} \cdot 3 x^{2} : \frac{18 x ^{2}}{1 - x ^{6}}

= \frac{18 x ^{2}}{1 - x ^{6}}

Popular Examples

derivative of (1+cos(2x)^2)

\frac{d}{d x} ((1 + cos (2 x))^{2})

derivative of (x^2-2sqrt(x)/x)

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

tangent of f(x)=sqrt(x^2+3x),(1,2)tangent of

f (x) = x^{2} + 3 x, (1, 2)

integral of (9-9x)/(1-sqrt(x))

\int \frac{9 - 9 x}{1 - x} d x

tangent of y=sqrt(x),\at x=4 tangent of

y = x, at x = 4

Frequently Asked Questions (FAQ)

What is the derivative of 6arcsin(x^3) ?
The derivative of 6arcsin(x^3) is (18x^2)/(sqrt(1-x^6))
What is the first derivative of 6arcsin(x^3) ?
The first derivative of 6arcsin(x^3) is (18x^2)/(sqrt(1-x^6))