Find the derivative of g(x) = 3tan (5bx)- 1/6 (squareroot of 12ax⁴+1) note that a is a constant.

Use implicit differentiation to find dy/dx given that y is defined implicitly by the equation

x² - 2xy² +y +5 =0

What is the slope of the tangent to the graph of y at (1,2)

The equation of the tangent to the graph of f at (1,2)

you are given the function f(x) = x³ - 6x². Find its critical point and establish the nature of each one.

Determine the derivative of f(x) = x ln (3+ax²)+ 4e^-1/2x2 secbx where a and b are constants