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Popular >

derivative of arctan(sqrt(5x^2-1))

Solution

derivative of

arctan (5 x^{2} - 1)

Solution

\frac{1}{x 5 x ^{2} - 1}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{x 5 x ^{2} - 1}

Popular Examples

(d^2y)/(dx^2)+2(dy)/(dx)=1+9x^2

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} = 1 + 9 x^{2}

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\int 3 sec^{4} (x) d x

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x \to \frac{3 π}{4} lim (- 2 sec (x))

(dx)/(dt)=6*0.3-5*x/(100+t),x(0)=0

\frac{d x}{d t} = 6 \cdot 0.3 - 5 \cdot \frac{x}{100 + t}, x (0) = 0

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Frequently Asked Questions (FAQ)

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