Question

Differentiate f(x) = sin x + 1/9 cot x f'(x) = Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the outer function y = f(y).] y = cubicroot 1 + 4x (g(x), f(u)) = () Find the derivative dy/dx = Find the derivative of the function. y =ᵃ³ + ᶜᵒˢ³x y'(x) =

Answer 1

To differentiate the function y = sin(x) + 1/9 cot(x), we use the sum rule and the derivative of cot(x) which is -csc^2(x). For the function y = a^3 + cos^3(x), we use the power rule and the chain rule.

Step-by-step explanation:

To differentiate the function y = sin(x) + 1/9 cot(x), we can use the sum rule and the derivative of cot(x) which is -csc^2(x). The derivative of sin(x) is cos(x), so the derivative of y is dy/dx = cos(x) - (1/9)csc^2(x).

To differentiate the function y = a^3 + cos^3(x), we can use the power rule and the chain rule. The power rule states that the derivative of a^3 is 3a^2, and the derivative of cos^3(x) is -3cos^2(x)sin(x). Therefore, the derivative of y is dy/dx = 3a^2 - 3cos^2(x)sin(x).