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Popular >

derivative of x^7arcsin(x)

Solution

derivative of

x^{7} arcsin (x)

Solution

7 x^{6} arcsin (x) + \frac{x ^{7}}{1 - x ^{2}}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{7}, g = arcsin (x)

= \frac{d}{d x} (x^{7}) arcsin (x) + \frac{d}{d x} (arcsin (x)) x^{7}

\frac{d}{d x} (x^{7}) = 7 x^{6}

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

= 7 x^{6} arcsin (x) + \frac{1}{1 - x ^{2}} x^{7}

\frac{1}{1 - x ^{2}} x^{7} = \frac{x ^{7}}{1 - x ^{2}}

= 7 x^{6} arcsin (x) + \frac{x ^{7}}{1 - x ^{2}}

Popular Examples

integral of (5x^2+7x+11)

\int (5 x^{2} + 7 x + 11) d x

integral from 0 to 1/2 of xcos(pix)

\int_{0}^{\frac{1}{2}} x cos (π x) d x

(\partial)/(\partial x)(cos^6(x^9y^8))

\frac{\partial}{\partial x} (cos^{6} (x^{9} y^{8}))

(\partial)/(\partial x)(ln(x^4+y^9))

\frac{\partial}{\partial x} (ln (x^{4} + y^{9}))

(\partial)/(\partial x)(x*e^{-y})

\frac{\partial}{\partial x} (x \cdot e^{- y})

Frequently Asked Questions (FAQ)

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