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Popular >

derivative of 7arcsin(x^3)

Solution

derivative of

7 arcsin (x^{3})

Solution

\frac{21 x ^{2}}{1 - x ^{6}}

Solution steps

\frac{d}{d x} (7 arcsin (x^{3}))

Take the constant out:

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

= 7 \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}

= 7 \cdot \frac{1}{1 - ( x ^{3} ) ^{2}} \cdot 3 x^{2}

Simplify

7 \cdot \frac{1}{1 - ( x ^{3} ) ^{2}} \cdot 3 x^{2} : \frac{21 x ^{2}}{1 - x ^{6}}

= \frac{21 x ^{2}}{1 - x ^{6}}

Popular Examples

derivative of y=(4t-1)(6t-3)^{-1}derivative of

y = (4 t - 1) (6 t - 3)^{- 1}

integral of (4x^4+x+1)/(x^5+x^4)

\int \frac{4 x ^{4} + x + 1}{x ^{5} + x ^{4}} d x

derivative of ln(225sin^2(x))derivative of

ln (225 sin^{2} (x))

tangent of y= 1/(sqrt(x))tangent of

y = \frac{1}{x}

integral from 1 to infinity of x^{-3}

\int_{1}^{\infty} x^{- 3} d x

Frequently Asked Questions (FAQ)

What is the derivative of 7arcsin(x^3) ?
The derivative of 7arcsin(x^3) is (21x^2)/(sqrt(1-x^6))
What is the first derivative of 7arcsin(x^3) ?
The first derivative of 7arcsin(x^3) is (21x^2)/(sqrt(1-x^6))