71 Calculus Tutorials

These Calculus tutorials are written by experienced educators, all of whom also offer private tutoring lessons. Get the Calculus help you need, whether through these tutorials or through private tutoring lessons.

Implicit differentiation

power rule d/dx(xn)=nx(n-1) chain rule (f(g(x))’=f'(g(x)).g(x)

Differentiate rational functions

d/dx(xn)=nx(n-1) d/dx(x)=1 d/dx(c)=0

Differentiating trigonometric function

(1) d/dx(sinx)= cosx (2) d/dx(cosx)= -sinx (3) d/dx(tanx)= -( secx)2 (4) d/dx(cotx)= -(cosecx)2 (5) d/dx(secx)= secx.tanx (6) d/dx(cosecx)= -cosecx.cotx

Differentiating trigonometric function

d/dx(sinx)=cosx d/dx(cosx)=-sinx d/dx(tanx)=(secx)2

Composite exponential function differentiation

When we differentiate the composite exponential function, we want to use the product rule and the chain rule.

Composite exponential function differentiation

product rule chain rule d/dx(ax)=ln(a).ax

Composite exponential function differentiation

product rule chain rule ln(a)m=m(ln)a

implicit differentiation

Evaluating derivative with implicit differentiation.

Second Derivative

NOTATION FOR SECOND DERIVATIVE Leibniz’s notation is d2y/dx2 Lagrange’s notation is f”

chain rule twice

The chain rule tells us how to take the derivative of their composition. d/dx(f(g(x)))=f'(g(x)).g'(x)