Implicit Differentiation

Warm Up

Find the derivative f(t) = (t² + 2t)⁵

Which of the following equations, if any, are written in implicit form?

(Check all that apply)

Differentiate with respect to x

$$y\ ^7$$  

Differentiate w.r.t.x

$$x^2+y^2+2$$  

Find  $$\frac{dy}{dx}$$ :  $$5x^2\ =3y^2+1$$  

Find  $$\frac{dy}{dx}$$ :  $$y^2=10x$$  

Find   $$\frac{dy}{dx}$$  :  $$2x^2-3y^2=4$$  

Find the derivative of $$x^2+xy+y^3=0$$  

Find dy/dx at the given point

x³ +2xy -y²=11 at (2,3)

Find the slope of the tangent line at the given point

x³ +2xy -y²=11 at (2,3)

Warm Up

The United Arab Emirates just launched its first ever mission to Mars

depend to the equation

$$x^2+y^3-2y=3$$  

, find the slope of the tangent line at the point (2,1).

A spherical snowball is rolled in fresh snow, causing it to grow so that its radius increases at a rate of 4 in/sec. How fast is the volume of the snowball increasing when the radius is 9 in?