If , by the chain rule, the derivative is . Further, ( where y is such that f(y)= x. Here, so . g(x) will be the value, y, such that f(y)= . Fortunately, it is clear that y= 1 satisfies that equation so
Let f(x)=(x^4)+(x^3)+1
Let g(x) be the inverse of f(x) and define F(x)=f(2g(x)). Find an equation for the tangent line to y=F(x) at x=3.
The answer the book gives is y=(88x-89)/7 I just have no clue how to get there! Please help!
If , by the chain rule, the derivative is . Further, ( where y is such that f(y)= x. Here, so . g(x) will be the value, y, such that f(y)= . Fortunately, it is clear that y= 1 satisfies that equation so