What is the derivative of (arcsin(5x+5))^8 ?

The derivative of (arcsin(5x+5))^8 is (40arcsin^7(5x+5))/(sqrt(-25x^2-50x-24))

What is the first derivative of (arcsin(5x+5))^8 ?

The first derivative of (arcsin(5x+5))^8 is (40arcsin^7(5x+5))/(sqrt(-25x^2-50x-24))

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derivative of

(arcsin (5 x + 5))^{8}

\frac{40 arcsin ^{7} ( 5 x + 5 )}{- 25 x ^{2} - 50 x - 24}

Solution steps

\frac{d}{d x} ((arcsin (5 x + 5))^{8})

Apply the chain rule:

8 (arcsin (5 x + 5))^{7} \frac{d}{d x} (arcsin (5 x + 5))

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

\frac{d}{d x} (arcsin (5 x + 5)) = \frac{5}{- 25 x ^{2} - 50 x - 24}

= 8 (arcsin (5 x + 5))^{7} \frac{5}{- 25 x ^{2} - 50 x - 24}

Simplify

8 arcsin^{7} (5 x + 5) \frac{5}{- 25 x ^{2} - 50 x - 24} : \frac{40 arcsin ^{7} ( 5 x + 5 )}{- 25 x ^{2} - 50 x - 24}

= \frac{40 arcsin ^{7} ( 5 x + 5 )}{- 25 x ^{2} - 50 x - 24}

x \to - 2 lim ((x + 4)^{3})

\frac{d}{d x} (30 x^{4} - 80 x^{3} + 60 x^{2} - 10)

\frac{d}{d x} (3 x - 4 x^{\frac{7}{8}})

x \to 0 lim (\frac{( 4 e ^{x} - 4 )}{x})

\frac{d}{d x} (sin (2 x^{2} \cdot e^{- x}))

What is the derivative of (arcsin(5x+5))^8 ?
The derivative of (arcsin(5x+5))^8 is (40arcsin^7(5x+5))/(sqrt(-25x^2-50x-24))
What is the first derivative of (arcsin(5x+5))^8 ?
The first derivative of (arcsin(5x+5))^8 is (40arcsin^7(5x+5))/(sqrt(-25x^2-50x-24))