Power rule, basic derivative rules and derivatives of sin x, cos x, eˣ and ln x

Learning objectives

Apply the power rule d/dx[xⁿ] = nxⁿ⁻¹ for any real exponent n, rewriting radicals and reciprocals as powers first

Differentiate constants, constant multiples, sums and differences of functions, and use these rules to differentiate any polynomial

Recall and apply the derivatives of sin x, cos x, eˣ and ln x, and combine them with the basic rules

Find the equation of the tangent line and the normal line to a curve at a given point, and find the points on a curve where the tangent has a specified slope

Use derivative rules together with values from a table or a graph of f and f′ to find derivatives of combinations of functions at specific points