What is the derivative of sqrt(1-289x^2)arccos(17x) ?

The derivative of sqrt(1-289x^2)arccos(17x) is -(289xarccos(17x))/(sqrt(1-289x^2))-17

What is the first derivative of sqrt(1-289x^2)arccos(17x) ?

The first derivative of sqrt(1-289x^2)arccos(17x) is -(289xarccos(17x))/(sqrt(1-289x^2))-17

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derivative of

1 - 289 x^{2} arccos (17 x)

- \frac{289 x arccos ( 17 x )}{1 - 289 x ^{2}} - 17

Solution steps

\frac{d}{d x} (1 - 289 x^{2} arccos (17 x))

Apply the Product Rule:

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

f = 1 - 289 x^{2}, g = arccos (17 x)

= \frac{d}{d x} (1 - 289 x^{2}) arccos (17 x) + \frac{d}{d x} (arccos (17 x)) 1 - 289 x^{2}

\frac{d}{d x} (1 - 289 x^{2}) = - \frac{289 x}{1 - 289 x ^{2}}

\frac{d}{d x} (arccos (17 x)) = - \frac{17}{1 - 289 x ^{2}}

= (- \frac{289 x}{1 - 289 x ^{2}}) arccos (17 x) + (- \frac{17}{1 - 289 x ^{2}}) 1 - 289 x^{2}

Simplify

(- \frac{289 x}{1 - 289 x ^{2}}) arccos (17 x) + (- \frac{17}{1 - 289 x ^{2}}) 1 - 289 x^{2} : - \frac{289 x arccos ( 17 x )}{1 - 289 x ^{2}} - 17

= - \frac{289 x arccos ( 17 x )}{1 - 289 x ^{2}} - 17

h \to 0 lim \frac{( ( \frac{1}{1 - ( x + h )} ) - ( \frac{1}{1 - x} ) )}{h}

\frac{d}{d x} (\frac{1}{( x + y )})

x \to + 0 + lim ((1 + x)^{(\frac{1}{x})})

\frac{d y}{d x} = 1 + y - x

3 x^{2} - 6 x - 9, at x = 3

What is the derivative of sqrt(1-289x^2)arccos(17x) ?
The derivative of sqrt(1-289x^2)arccos(17x) is -(289xarccos(17x))/(sqrt(1-289x^2))-17
What is the first derivative of sqrt(1-289x^2)arccos(17x) ?
The first derivative of sqrt(1-289x^2)arccos(17x) is -(289xarccos(17x))/(sqrt(1-289x^2))-17