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Popular >

derivative of arcsin(9x^5)

Solution

\frac{d}{d x} (arcsin (9 x^{5}))

Solution

\frac{45 x ^{4}}{1 - 81 x ^{10}}

Solution steps

\frac{d}{d x} (arcsin (9 x^{5}))

Apply the chain rule:

\frac{1}{1 - ( 9 x ^{5} ) ^{2}} \frac{d}{d x} (9 x^{5})

= \frac{1}{1 - ( 9 x ^{5} ) ^{2}} \frac{d}{d x} (9 x^{5})

\frac{d}{d x} (9 x^{5}) = 45 x^{4}

= \frac{1}{1 - ( 9 x ^{5} ) ^{2}} \cdot 45 x^{4}

Simplify

\frac{1}{1 - ( 9 x ^{5} ) ^{2}} \cdot 45 x^{4} : \frac{45 x ^{4}}{1 - 81 x ^{10}}

= \frac{45 x ^{4}}{1 - 81 x ^{10}}

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\int e^{x} sin (yz) d x

integral of (x-1)/(x^2-2x+4)

\int \frac{x - 1}{x ^{2} - 2 x + 4} d x

(dy)/(dx)=(9x)/(10y)

\frac{d y}{d x} = \frac{9 x}{10 y}

(\partial}{\partial x}(\frac{V(x))/x)

\frac{\partial}{\partial x} (\frac{V ( x )}{x})

Frequently Asked Questions (FAQ)

What is the derivative of arcsin(9x^5) ?
The derivative of arcsin(9x^5) is (45x^4)/(sqrt(1-81x^{10))}
What is the first derivative of arcsin(9x^5) ?
The first derivative of arcsin(9x^5) is (45x^4)/(sqrt(1-81x^{10))}