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.

exponential function

y=v(u(x)) — dy/dx=v'(u(x)).u'(x) (1) d/dx(sinx)=cosx (2) d/dx(cosx)=-sinx (3) d/dx(tanx)=(secx)2

Differentiating related function

d/dt(sinx(t))=d/dx(sinx).dx/dt d/dt(cosy(t))=d/dy(cosy).dy/dt

Differentiating using multiple rules

We will need to use the product rule and chain rule

Differentiating using multiple rule

using the chain rule and product rule

Parametric functions differentiation

In general, to find the derivative of a function defined parametrically by the equations x=u(t), y=v(t), we use the following rule dy/dx=(dy/dt).(dt/dx)=v(t)/u(t)

Second Derivative parametric function

x=u(t) dx/dt=U'(t) y=v(t) dy/dt=v'(t) dy/dx=dy/dt.dt/dx d2y/dx2=d/dt(dy/dx).dt/dx

Negative power differentiation

We can rewrite each rational term in the expression as a negative power of x

Derivatives of inverse trigonometric function

the formula for the derivative of arctan(x)=1/(1+x2).

Implicit differentiation

In implicit differentiation, we differentiate both sides of the equation according to x and treat y as an implicit function of x

Implicit differentiation(advanced)

d/dx(sinx)=cosx d/dx(y)=1.dy/dx