mesa said:Homework Statement
cos(x-y) = (x)(invcot 2x) + 6^(3x^2 + 2x)
Homework Equations
I'm not sure how to get y to one side, otherwise I think I could handle the derivation
The Attempt at a Solution
So far I have
(cos x)(cos y) + (sin x)(sin y) = (x)(invcot 2x) + 6^(3x^2 + 2x)
I know, not much :)
There is no good reason to "reduce" cos(x- y) nor to solve for y. The (partial) derivative of cos(x- y), with respect to x, is -sin(x- y) and the (partial) derivative with respect to y is sin(x- y).mesa said:Homework Statement
cos(x-y) = (x)(invcot 2x) + 6^(3x^2 + 2x)
Homework Equations
I'm not sure how to get y to one side, otherwise I think I could handle the derivation
The Attempt at a Solution
So far I have
(cos x)(cos y) + (sin x)(sin y) = (x)(invcot 2x) + 6^(3x^2 + 2x)
I know, not much :)
A derivative is a mathematical concept that represents the rate of change of a function at a specific point. It measures how much a function is changing, or its slope, at a particular point. It is commonly used in calculus to solve problems involving rates of change, optimization, and approximation.
The derivative of a function helps us understand the behavior of the function at any given point. It allows us to determine the rate of change, which is important in many real-world applications such as physics, economics, and engineering. Additionally, the derivative is used to find the maximum and minimum values of a function, which is crucial in optimization problems.
The process of finding a derivative is called differentiation. It involves using various rules and formulas to find the derivative of a function. These rules include the power rule, product rule, chain rule, and quotient rule. The steps for finding a derivative include identifying the function, applying the appropriate rule, and simplifying the resulting expression.
The chain rule is used when the function is composed of two or more functions. It allows us to find the derivative of the outer function while taking into account the derivative of the inner function. In other words, it helps us find the derivative of a function within a function.
Yes, derivatives can be negative. A negative derivative indicates that the function is decreasing at a particular point. This is because the derivative represents the slope of the function, and a negative slope means the function is decreasing. However, a negative derivative does not necessarily mean that the function is always decreasing, as it can change from positive to negative or vice versa at different points.