- #1
meeklobraca
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Homework Statement
f(x) = sin(5x) / cos(x^2)
Homework Equations
The Attempt at a Solution
I got 25Cosx-Sin 5xCosx / cos x^3
Would this be the correct answer?
Thanks!
meeklobraca said:Is the denominator 2Cos(x^2)?
meeklobraca said:I see what your saying. I meant for all of that to be divided by Cos^2(x^2)
The derivative of a function is a measure of how the output value of the function changes with respect to the input value. It represents the slope of the function at a specific point.
Finding the derivative is important because it allows us to analyze the behavior of a function and make predictions about its values. It also helps us solve problems in fields such as physics, engineering, and economics.
The derivative of a function can be found using the rules of differentiation, such as the power rule, product rule, and chain rule. These rules involve taking the limit of the difference quotient as the change in the input value approaches zero.
Yes, the derivative of a function can be negative. This means that the function is decreasing at that point, and the slope of the tangent line is negative. A negative derivative can also indicate concave down behavior.
Yes, there is a difference between derivative and differentiation. Derivative refers to the output value of the process of differentiation, which is the instantaneous rate of change of the function at a specific point. Differentiation, on the other hand, is the process of finding the derivative of a function.