The linearity rule and the product rule will be justified at the end of the section; a proof of the extended power rule appears in the section on the chain rule. Example 2 Let. Example 4 Let. Find f ' x. Solve equations and inequalities Simplify expressions Factor polynomials Graph equations and inequalities Advanced solvers All solvers Tutorials. Partial Fractions. Welcome to Quickmath Solvers! Enter an expression and the variable to differentiate with respect to.
Then click the Differentiate button. Some basic rules exist with regard to differentiating functions. Differentiate a constant function. The derivative of a constant is zero. Apply the power rule to differentiate a function. Find the derivative of a function using the product rule.
Rather, the derivative of a product of two functions is the first times the derivative of the second, plus the second times the derivative of the first.
Get the derivative of a function using the quotient rule. A quotient is one function divided by another. The derivative of a quotient equals the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, then divided by the denominator squared. The general rule for differentiation is:. When calculating the rate of change or the gradient of a tangent to a curve, we are required to write the final answer to the differentiated expression without negative or fractional powers.
Doing so makes it much easier to evaluate for specific values without a calculator. To remove negative and fractional powers, we need to recall the laws of indices. The two that will be useful here are:.
Therefore the gradient of the tangent to the curve is 1. The previous examples have very simple expressions.
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