Chapter 3, Problem 67RE

Implicit Differentiation The equation for the curve graphed to the left is x3 - y3 – 6xy = 0. Keep in mind that y is a function of x. When we take the derivative of y we need to use the chain rule because y depends on x: it may help to write it as Use implicit differentiation to find in terms of the -4 -2 variables x and y.

derivative of the function

Evaluate the second derivative of the function at the given point. Use a computer algebra system to verify your result. (0,33) f"(0) = f(x) = Need Help? 7 √x + 9 Read It

Differentiate the function. Then find an equation of the tangent line at the indicated point on the graph of the function. y = f(x)=3+√√1-x, (x,y)= (-3,5) The derivative of the function y = f(x) = 3+√√1-x is What is the equation of the tangent line at (-3,5)? O A. 1 y-5= (x+3) O C. y-5-4(x + 3) B. y-5= 4(x + 3) D. 1 y-5=(x+3)

Find the derivative of the function using the definition of derivative. 1 g(x) 3 + 1 g'(x) = (3+ vx (2vx) State the domain of the function. (Enter your answer using interval notation.) State the domain of its derivative. (Enter your answer using interval notation.) Need Help? Read It