No AI is used
  1. Home
  2. Calculators
  3. Calculators: Calculus I
  4. Calculus Calculator

Derivative of $$$6 \theta$$$

The calculator will find the derivative of $$$6 \theta$$$, with steps shown.

Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps

Leave empty for autodetection.
Leave empty, if you don't need the derivative at a specific point.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please contact us.

Your Input

Find $$$\frac{d}{d\theta} \left(6 \theta\right)$$$.

Solution

Apply the constant multiple rule $$$\frac{d}{d\theta} \left(c f{\left(\theta \right)}\right) = c \frac{d}{d\theta} \left(f{\left(\theta \right)}\right)$$$ with $$$c = 6$$$ and $$$f{\left(\theta \right)} = \theta$$$:

$${\color{red}\left(\frac{d}{d\theta} \left(6 \theta\right)\right)} = {\color{red}\left(6 \frac{d}{d\theta} \left(\theta\right)\right)}$$

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

$$6 {\color{red}\left(\frac{d}{d\theta} \left(\theta\right)\right)} = 6 {\color{red}\left(1\right)}$$

Thus, $$$\frac{d}{d\theta} \left(6 \theta\right) = 6$$$.

Answer

$$$\frac{d}{d\theta} \left(6 \theta\right) = 6$$$A

Related Notes: Definition of Derivative , Derivatives of Elementary Functions , Table of Derivatives , Related Rates , Studying Derivative Graphically , Optimization Problems , Applications to Economics , Constant Multiple Rule , Sum and Difference Rules , Product Rule , Quotient Rule , Chain Rule , Derivative of Inverse Function