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Popular >

derivative of arccos(5x^8)

Solution

derivative of

arccos (5 x^{8})

Solution

- \frac{40 x ^{7}}{1 - 25 x ^{16}}

Solution steps

\frac{d}{d x} (arccos (5 x^{8}))

Apply the chain rule:

- \frac{1}{1 - ( 5 x ^{8} ) ^{2}} \frac{d}{d x} (5 x^{8})

= - \frac{1}{1 - ( 5 x ^{8} ) ^{2}} \frac{d}{d x} (5 x^{8})

\frac{d}{d x} (5 x^{8}) = 40 x^{7}

= - \frac{1}{1 - ( 5 x ^{8} ) ^{2}} \cdot 40 x^{7}

Simplify

- \frac{1}{1 - ( 5 x ^{8} ) ^{2}} \cdot 40 x^{7} : - \frac{40 x ^{7}}{1 - 25 x ^{16}}

= - \frac{40 x ^{7}}{1 - 25 x ^{16}}

Popular Examples

derivative of (7x^2-1/x)

\frac{d}{d x} (\frac{7 x ^{2} - 1}{x})

y^{''}+4y=0,y(0)=1,y^'(0)=4

y^{^{''}} + 4 y = 0, y (0) = 1, y^{^{'}} (0) = 4

(dy)/(dx)=32x^3y^3,y(0)=k

\frac{d y}{d x} = 32 x^{3} y^{3}, y (0) = k

integral of [(a^3)/(x^2+a^2)]^2

\int [\frac{a ^{3}}{x ^{2} + a ^{2}}]^{2} d x

limit as x approaches 4 of 3x+5

x \to 4 lim (3 x + 5)

Frequently Asked Questions (FAQ)

What is the derivative of arccos(5x^8) ?
The derivative of arccos(5x^8) is -(40x^7)/(sqrt(1-25x^{16))}
What is the first derivative of arccos(5x^8) ?
The first derivative of arccos(5x^8) is -(40x^7)/(sqrt(1-25x^{16))}