Question

Let f(x) = 9sin x + 7cos x. Find f'(x) and f'(11π/6).

Answer 1

The derivative of f(x) = 9sin x + 7cos x is f'(x) = 9cos x - 7sin x. To find f'(11π/6), substitute x = 11π/6 into the equation.

Step-by-step explanation:

To find the derivative of f(x) = 9sin x + 7cos x, we can use the chain rule. The derivative of sin x is cos x, and the derivative of cos x is -sin x. So:

• f'(x) = 9cos x - 7sin x

To find f'(11π/6), we substitute x = 11π/6 into the equation f'(x) = 9cos x - 7sin x:

• f'(11π/6) = 9cos(11π/6) - 7sin(11π/6)
• = 9(cos π/6) - 7(sin π/6)
• = 9(√3/2) - 7(1/2)
• = 9√3/2 - 7/2