Derivative of r*cos(theta) with respect to r

The calculator will find the derivative of

r \cos{\left(\theta \right)}

with respect to

r

, with steps shown.

Your Input

Find $\frac{d}{dr} \left(r \cos{\left(\theta \right)}\right)$ .

Solution

Apply the constant multiple rule $\frac{d}{dr} \left(c f{\left(r \right)}\right) = c \frac{d}{dr} \left(f{\left(r \right)}\right)$ with $c = \cos{\left(\theta \right)}$ and $f{\left(r \right)} = r$ :

{\color{red}\left(\frac{d}{dr} \left(r \cos{\left(\theta \right)}\right)\right)} = {\color{red}\left(\cos{\left(\theta \right)} \frac{d}{dr} \left(r\right)\right)}

Apply the power rule $\frac{d}{dr} \left(r^{n}\right) = n r^{n - 1}$ with $n = 1$ , in other words, $\frac{d}{dr} \left(r\right) = 1$ :

\cos{\left(\theta \right)} {\color{red}\left(\frac{d}{dr} \left(r\right)\right)} = \cos{\left(\theta \right)} {\color{red}\left(1\right)}

Thus, $\frac{d}{dr} \left(r \cos{\left(\theta \right)}\right) = \cos{\left(\theta \right)}$ .

Answer

$\frac{d}{dr} \left(r \cos{\left(\theta \right)}\right) = \cos{\left(\theta \right)}$ A

Derivative of rcos⁡(θ)r \cos{\left(\theta \right)}rcos(θ) with respect to rrr

Your Input

Solution

Answer

Derivative of $r \cos{\left(\theta \right)}$ with respect to $r$