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Popular >

derivative of 7arcsin(x^3)

Solution

\frac{d}{d x} (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

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f (x) = \frac{1}{( e ^{x} ) ^{3}}

integral from 0 to 1 of (1+12x)/(1+3x)

\int_{0}^{1} \frac{1 + 12 x}{1 + 3 x} d x

(\partial)/(\partial x)(sin(2x-y))

\frac{\partial}{\partial x} (sin (2 x - y))

derivative of x^2-3x+1

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

limit as x approaches 0 of e^{-3x}

x \to 0 lim (e^{- 3 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))