Calculus

Derivatives

Derivative by First Principle

         

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

If f(x)=x2+7x,f(x)=x^2+7x, what is the value of f(6)?f'(6)?

Find the derivative of f(x)=13x3f(x)=13x^3 using the definition of derivative

f(x)=limh0f(x+h)f(x)h. f'(x) = \lim_{h \rightarrow 0 } \frac{ f( x + h) - f(x) } { h }.

f(x)f(x) is a function differentiable at x=1x=1 and f(1)=115f'(1)=\frac{1}{15}. What is the value of limx1x31f(x)f(1)?\displaystyle \lim_{x \to 1} \frac{x^3-1}{f(x)-f(1)}?

Find the derivative of f(x)=2x2+3x+26f(x)=-2x^2+3x+26 from the definition

f(x)=limh0f(x+h)f(x)h. f'(x) = \lim_{h \rightarrow 0 } \frac{ f( x + h) - f(x) } { h } .

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