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Popular >

derivative of sqrt(r^2-16x^2)

Solution

derivative of

r^{2} - 16 x^{2}

Solution

- \frac{16 x}{r ^{2} - 16 x ^{2}}

Solution steps

\frac{d}{d x} (r^{2} - 16 x^{2})

Apply the chain rule:

\frac{1}{2 r ^{2} - 16 x ^{2}} \frac{d}{d x} (r^{2} - 16 x^{2})

= \frac{1}{2 r ^{2} - 16 x ^{2}} \frac{d}{d x} (r^{2} - 16 x^{2})

\frac{d}{d x} (r^{2} - 16 x^{2}) = - 32 x

= \frac{1}{2 r ^{2} - 16 x ^{2}} (- 32 x)

Simplify

\frac{1}{2 r ^{2} - 16 x ^{2}} (- 32 x) : - \frac{16 x}{r ^{2} - 16 x ^{2}}

= - \frac{16 x}{r ^{2} - 16 x ^{2}}

Popular Examples

(\partial)/(\partial x)(sqrt(y-x^2))

\frac{\partial}{\partial x} (y - x^{2})

(\partial)/(\partial x)(rcos(x))

\frac{\partial}{\partial x} (r cos (x))

limit as x approaches 7 of 3x-4

x \to 7 lim (3 x - 4)

(\partial)/(\partial x)((x^4)/(x^2+y^2))

\frac{\partial}{\partial x} (\frac{x ^{4}}{x ^{2} + y ^{2}})

integral of 2xsqrt(1-x^2)

\int 2 x 1 - x^{2} d x

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(r^2-16x^2) ?
The derivative of sqrt(r^2-16x^2) is -(16x)/(sqrt(r^2-16x^2))
What is the first derivative of sqrt(r^2-16x^2) ?
The first derivative of sqrt(r^2-16x^2) is -(16x)/(sqrt(r^2-16x^2))