What is the derivative of (1-25x^2)^2arcsin(5x) ?

The derivative of (1-25x^2)^2arcsin(5x) is -100xarcsin(5x)(1-25x^2)+5(-25x^2+1)^{3/2}

What is the first derivative of (1-25x^2)^2arcsin(5x) ?

The first derivative of (1-25x^2)^2arcsin(5x) is -100xarcsin(5x)(1-25x^2)+5(-25x^2+1)^{3/2}

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derivative of

(1 - 25 x^{2})^{2} arcsin (5 x)

- 100 x arcsin (5 x) (1 - 25 x^{2}) + 5 (- 25 x^{2} + 1)^{\frac{3}{2}}

Solution steps

\frac{d}{d x} ((1 - 25 x^{2})^{2} arcsin (5 x))

Apply the Product Rule:

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

f = (1 - 25 x^{2})^{2}, g = arcsin (5 x)

= \frac{d}{d x} ((1 - 25 x^{2})^{2}) arcsin (5 x) + \frac{d}{d x} (arcsin (5 x)) (1 - 25 x^{2})^{2}

\frac{d}{d x} ((1 - 25 x^{2})^{2}) = - 100 x (1 - 25 x^{2})

\frac{d}{d x} (arcsin (5 x)) = \frac{5}{1 - 25 x ^{2}}

= (- 100 x (1 - 25 x^{2})) arcsin (5 x) + \frac{5}{1 - 25 x ^{2}} (1 - 25 x^{2})^{2}

Simplify

(- 100 x (1 - 25 x^{2})) arcsin (5 x) + \frac{5}{1 - 25 x ^{2}} (1 - 25 x^{2})^{2} : - 100 x arcsin (5 x) (1 - 25 x^{2}) + 5 (- 25 x^{2} + 1)^{\frac{3}{2}}

= - 100 x arcsin (5 x) (1 - 25 x^{2}) + 5 (- 25 x^{2} + 1)^{\frac{3}{2}}

\frac{64}{x ^{2} + 16}, at x = 3

\int_{2}^{3} (x^{2} - 4) d x

f (x) = \frac{6 x}{2 + x ^{2}}, (2, 2)

\int (3 x + 2) d x

y = 19 cos (\frac{x}{b} - 2.5) + 19

What is the derivative of (1-25x^2)^2arcsin(5x) ?
The derivative of (1-25x^2)^2arcsin(5x) is -100xarcsin(5x)(1-25x^2)+5(-25x^2+1)^{3/2}
What is the first derivative of (1-25x^2)^2arcsin(5x) ?
The first derivative of (1-25x^2)^2arcsin(5x) is -100xarcsin(5x)(1-25x^2)+5(-25x^2+1)^{3/2}