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

The derivative of sqrt(1-25x^2)arccos(5x) is -(25xarccos(5x))/(sqrt(1-25x^2))-5

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

The first derivative of sqrt(1-25x^2)arccos(5x) is -(25xarccos(5x))/(sqrt(1-25x^2))-5

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

(- \frac{25 x}{1 - 25 x ^{2}}) arccos (5 x) + (- \frac{5}{1 - 25 x ^{2}}) 1 - 25 x^{2} : - \frac{25 x arccos ( 5 x )}{1 - 25 x ^{2}} - 5

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

What is the derivative of sqrt(1-25x^2)arccos(5x) ?
The derivative of sqrt(1-25x^2)arccos(5x) is -(25xarccos(5x))/(sqrt(1-25x^2))-5
What is the first derivative of sqrt(1-25x^2)arccos(5x) ?
The first derivative of sqrt(1-25x^2)arccos(5x) is -(25xarccos(5x))/(sqrt(1-25x^2))-5