What is the derivative of sqrt(r^2-5x^2) ?

The derivative of sqrt(r^2-5x^2) is -(5x)/(sqrt(r^2-5x^2))

What is the first derivative of sqrt(r^2-5x^2) ?

The first derivative of sqrt(r^2-5x^2) is -(5x)/(sqrt(r^2-5x^2))

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derivative of

r^{2} - 5 x^{2}

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (r^{2} - 5 x^{2}) = - 10 x

= \frac{1}{2 r ^{2} - 5 x ^{2}} (- 10 x)

Simplify

\frac{1}{2 r ^{2} - 5 x ^{2}} (- 10 x) : - \frac{5 x}{r ^{2} - 5 x ^{2}}

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

\int \frac{x}{1 + 3 x ^{2}} d x

\int (3 e^{x} + 8 x^{3} + 4 x) d x

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

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