Question
Constant Rule proof For the constant function $f(x)=c,$ use the definition of the derivative to show that $f^{\prime}(x)=0$
Step 1
The derivative of a function $f(x)$ at a point $x$ is given by the limit: \[f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}\] Show more…
Show all steps
Your feedback will help us improve your experience
Anna Waldram and 69 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
For the constant function $f(x)=c,$ use the definition of the derivative to show that $f^{\prime}(x)=0$.
Derivatives
Rules of Differentiation
Use the Product Rule to show that $\frac{d}{d x}(c \cdot f(x))=c \cdot \frac{d}{d x} f(x)$ for any constant c.
Rules for Differentiation
Suppose that $f^{\prime}(x)=f(x)$ for all $x .$ Prove that $f(x)=$ $\left.\mathrm{Ce}^{x} \text { for some constant } C . \text { [Hint: Consider } f(x) / e^{x} .\right]$
Short-Cuts to Differentiation
Theorems About Differentiable Functions
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD