You have to use the given values, yes, but except for A and C, you need to take the derivative using either the chain rule (B and D) or quotient rule (E).kxpatel29 said:Homework Statement
Given F(2)=5, F'(2)=6, F(4)=3, F'(4)=6 and G(3)=6, G'(3)=3, G(4)=2, G'(4)=1
A. H(4) if H(x)=F(G(x)) = ?
B. H'(4) if H(x)=F(G(x)) = ?
C. H(4) if H(x)=G(F(x)) = ?
D. H'(4) if H(x)=G(F(x)) =?
E. H'(4) if H(x)=F(x)/G(x) =?
Homework Equations
My teacher did not teach this yet, so I have no idea. My book doesn't even cover this
The Attempt at a Solution
Would we just use the given values? For E, F(x)/G(x)=1/2?
Derivatives in Calculus 2 refer to the rate of change of a function at a specific point. They are used to calculate the slope of a tangent line to a curve at a given point and can also represent the instantaneous rate of change of a function.
To find derivatives in Calculus 2, you can use various methods such as the power rule, product rule, quotient rule, and chain rule. It is important to also understand the concept of limits and how they are used to calculate derivatives.
The main purpose of finding derivatives in Calculus 2 is to analyze the behavior of functions and solve real-world problems involving rates of change. Derivatives can also help in finding maximum and minimum values of functions.
Sure, let's say we have the function f(x) = 2x^3 + 4x^2 - 3x + 5. To find the derivative of this function, we would use the power rule to get f'(x) = 6x^2 + 8x - 3. This tells us the slope of the tangent line at any given point on the original curve.
Some common mistakes to avoid when finding derivatives in Calculus 2 include not understanding the basic concepts and rules, not simplifying expressions before finding the derivative, and making calculation errors. It is also important to pay attention to the domain of the function and any restrictions when finding derivatives.