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Willian93
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Homework Statement
if p(x)= f(x^3), find P'(1)
Homework Equations
The Attempt at a Solution
can i do the derivative of x^3 is 2x^2, then substitute to get f(2x^2)?, then substitute 1 for x?
Willian93 said:Homework Statement
if p(x)= f(x^3), find P'(1)
Willian93 said:can i do the derivative of x^3 is 2x^2, then substitute to get f(2x^2)?, then substitute 1 for x?
No. The chain rule says that the derivative of f(g(x)) is f'(g(x))g'(x). (And, as Cepheid said, the derivative of x^3 is NOT "2x^2".)Willian93 said:Homework Statement
if p(x)= f(x^3), find P'(1)
Homework Equations
The Attempt at a Solution
can i do the derivative of x^3 is 2x^2, then substitute to get f(2x^2)?, then substitute 1 for x?
HallsofIvy said:(And, as Cepheid said, the derivative of x^3 is NOT "2x^2".)
The formula for finding the derivative of a function is f'(x) = lim(h->0) [f(x+h) - f(x)]/h. This is known as the definition of the derivative.
P'(1) represents the derivative of the function P(x) at x=1. In other words, it is the slope of the tangent line to the graph of P(x) at the point (1, P(1)).
To find the derivative of a function that is defined by a composition of two functions, we use the chain rule. The chain rule states that if y=f(g(x)), then y' = f'(g(x)) * g'(x).
Finding the derivative of a function is important because it tells us the rate of change of the function at a specific point. This can be useful in determining the slope of a curve, the velocity of an object, or the growth rate of a population.
To find the derivative of a polynomial function, we use the power rule. The power rule states that if y = ax^n, then y' = nax^(n-1). In other words, we multiply the coefficient by the exponent and decrease the exponent by 1.