What is the derivative of arctan(sqrt(-5x+1)) ?

The derivative of arctan(sqrt(-5x+1)) is -5/(2(-5x+2)sqrt(-5x+1))

What is the first derivative of arctan(sqrt(-5x+1)) ?

The first derivative of arctan(sqrt(-5x+1)) is -5/(2(-5x+2)sqrt(-5x+1))

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\frac{d}{d x} (arctan (- 5 x + 1))

- \frac{5}{2 ( - 5 x + 2 ) - 5 x + 1}

Solution steps

\frac{d}{d x} (arctan (- 5 x + 1))

Apply the chain rule:

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

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

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

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

Simplify

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

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

f (x) = 3 x^{2} + 5 x - 6

f (x) = arcsin (\frac{x}{3})

\frac{d}{d x} (\frac{6 x}{7 - cot ( x )})

\frac{\partial}{\partial x} (x^{yz})

\frac{d}{d x} (\frac{- 6}{x ^{4}})

What is the derivative of arctan(sqrt(-5x+1)) ?
The derivative of arctan(sqrt(-5x+1)) is -5/(2(-5x+2)sqrt(-5x+1))
What is the first derivative of arctan(sqrt(-5x+1)) ?
The first derivative of arctan(sqrt(-5x+1)) is -5/(2(-5x+2)sqrt(-5x+1))