Question

How do you differentiate `y = 10cosx`?

Answer 1

`d/dx10cosx=-10sinx`

Explanation:

From the rules of differentiation, the derivative of a constant times a function is the constant times the derivative of the function.
So `d/dx(10cosx) =10d/dx cosx`

Then from the rules of differentiation for trigonometric functions, the derivative of the cosine of a function is the negative sine of the function multiplied by the derivative of the function.
`therefore d/dxcosx = -sinx*d/dxx`

since x can be written as `x^1`, it is a polynomial function and so its derivative is the power times the function raised to1 less than the given power, that is
`d/dxx^1=1x^0=1`
Hence the overall answer is `d/dx10cosx=-10sinx`