Derivatives

Concepts

• Derivative 20 exercisesThe derivative of f at a is the limit of the difference quotient as h→0. It measures the instantaneous rate of change and is the…
• Tangent line 10 exercisesThe tangent line to the graph of f at the point (a,f(a)) is the line through that point with slope f^prime(a). It is the best lin…
• Basic differentiation rules 10 exercisesThe derivative of a constant is 0 and that of x^n is n x^n-1. The derivative is also linear: the derivative of a sum is the sum o…
• Product rule 10 exercisesRule giving the derivative of a product of two differentiable functions: (fg)^prime=f^primeg+fg^prime. It is not the product of t…
• Quotient rule 10 exercisesThe derivative of a quotient (f)/(g), with gne0, is (f^primeg-fg^prime)/(g^2).
• Chain rule 10 exercisesThe chain rule gives the derivative of a composition f(g(x)): the outer derivative evaluated at the inner function, times the der…
• Derivatives of trigonometric functions 10 exercisesThese are the derivatives of sine, cosine and tangent, with angles in radians; the others follow from the quotient and chain rule…
• Derivatives of exponentials and logarithms 10 exercisesThe function e^x is its own derivative. For base a>0, a^x has derivative a^xln a, and ln x has derivative (1)/(x) for x>0.
• Implicit differentiation 10 exercisesWhen y is defined implicitly by an equation in x and y, both sides are differentiated with respect to x, remembering that y depen…