Compute the derivative with respect to x of
y = 2 sin x cos x
Solution
Use implicit differentiation to compute the derivative of y with respect to x if
Solution Differentiating both sides with respect to x gives
Solving for gives
Use a linear approximation to show that near x = 0
Solution Apply the linearization formula
with and x0 = 0:
Compute the derivative with respect to x of
Solution The easiest method is logarithmic differentiation.
Differentiating both sides with respect to x gives
One of the lines tangent to the graph of y = ex passes through the origin. Find the equation of that tangent line.
Solution If the tangent line attaches to the curve at it has slope and equation
The requirement that the tangent line pass through the origin forces
a = 1
The equation of the tangent line is
y = e x