It is against Physics Forums policy to provide answers to posters' questions.omkar13 said:I think the question is ((cosx)^3)*sin(x).Am I right?The formula for d(uv)/dx=u(dv/dx)+v(du/dx).And of course I think you need only formula.Do you need answer?
The derivative of cos^3(x)*sin(x) is -3cos^2(x)sin^2(x) + cos^3(x)cos(x).
To find the derivative of cos^3(x)*sin(x), you can use the product rule, which states that the derivative of a product is equal to the first function times the derivative of the second function plus the second function times the derivative of the first function.
Yes, you can simplify the derivative of cos^3(x)*sin(x) to -3sin(x)cos^4(x) + cos^4(x).
The derivative of cos^3(x)*sin(x) at a specific point can be found by plugging in the x-value of the point into the simplified derivative expression.
The graph of cos^3(x)*sin(x) and its derivative are related because the derivative represents the rate of change of the original function. This means that the derivative will have the same critical points (maxima, minima, points of inflection) as the original function, but at these points, the derivative will be either 0 or undefined.