3. Techniques of Differentiation

Find the derivative of each function.

$y=(3x+5)^2$

Find the derivative of each function.

$f\left(t\right)=2t(t^{-3}+t^{2/3})$

Find the derivative of the function.

$y=\frac{2-3t}{4t^2+7}$

Find the derivative of the function.

$f\left(x\right)=\frac{2x-1}{x^3+2}$

{Use of Tech} The Witch of Agnesi The graph of y = a³ / (x² + a²), where a is a constant, is called the witch of Agnesi (named after the 18th-century Italian mathematician Maria Agnesi).

Let a = 3 and find an equation of the line tangent to y = 27 / (x² + 9) at x = 2.

Derivative calculations Evaluate the derivative of the following functions at the given point.

f(t) = 1/t+1; a=1

Evaluate dy/dx and dy/dx|x=2 if y= x+1/x+2

21–30. Derivatives

b. Evaluate f'(a) for the given values of a.

f(x) = 1/x+1; a = -1/2;5