Calculus

# Derivative by First Principle

If $f(x)=2x+5,$ what is the value of $f'(3)?$

If $f(x)=x^2+7x,$ what is the value of $f'(6)?$

Find the derivative of $f(x)=13x^3$ using the definition of derivative

$f'(x) = \lim_{h \rightarrow 0 } \frac{ f( x + h) - f(x) } { h }.$

$f(x)$ is a function differentiable at $x=1$ and $f'(1)=\frac{1}{15}$. What is the value of $\displaystyle \lim_{x \to 1} \frac{x^3-1}{f(x)-f(1)}?$

Find the derivative of $f(x)=-2x^2+3x+26$ from the definition

$f'(x) = \lim_{h \rightarrow 0 } \frac{ f( x + h) - f(x) } { h } .$

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