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Popular >

d/(d{r)}({r}sqrt(1-{r)^2})

Solution

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

Solution

1 - r^{2} - \frac{r ^{2}}{1 - r ^{2}}

Solution steps

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

Apply the Product Rule:

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

f = r, g = 1 - r^{2}

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

\frac{d}{d r} (r) = 1

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

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

Simplify

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

= 1 - r^{2} - \frac{r ^{2}}{1 - r ^{2}}

Popular Examples

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x \to \infty lim (2 x - 1)

y^'=y(1-y),y(0)=-2

y^{^{'}} = y (1 - y), y (0) = - 2

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\int \frac{y + 1}{y ^{2} + y + 1} d y

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\frac{\partial}{\partial z} (x cos (y) sin (z))

integral of (x^3)/(sqrt(x-1))

\int \frac{x ^{3}}{x - 1} d x

Frequently Asked Questions (FAQ)

What is the d/(d{r)}({r}sqrt(1-{r)^2}) ?
The d/(d{r)}({r}sqrt(1-{r)^2}) is sqrt(1-{r)^2}-({r}^2)/(sqrt(1-{r)^2)}
What is the first d/(d{r)}({r}sqrt(1-{r)^2}) ?
The first d/(d{r)}({r}sqrt(1-{r)^2}) is sqrt(1-{r)^2}-({r}^2)/(sqrt(1-{r)^2)}