Final Answer
Step-by-step Solution
Specify the solving method
Find the derivative of $y^3$ using the definition. Apply the definition of the derivative: $\displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$. The function $f(x)$ is the function we want to differentiate, which is $y^3$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
Learn how to solve problems step by step online.
$\lim_{h\to0}\left(\frac{y^3-y^3}{h}\right)$
Learn how to solve problems step by step online. Find the derivative of y^3 using the definition. Find the derivative of y^3 using the definition. Apply the definition of the derivative: \displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}. The function f(x) is the function we want to differentiate, which is y^3. Substituting f(x+h) and f(x) on the limit, we get. Cancel like terms y^3 and -y^3. Zero divided by anything is equal to zero. The limit of a constant is just the constant.