Explanation:
the derivative of the sum of terms in x is the same as the sum of the derivatives of the individual terms.
d/dx × (-4sin(x) + 9x) = d/dx × (-4sin(x)) + d/dx × (9x)
and also : the derivative of a term in x multiplied by a constant c is c × derivative of the term in x.
d/dx × (-4sin(x)) + d/dx × (9x) =
-4 × (d/dx × sin(x)) + 9 × (d/dx × x)
so, what is the derivative of sin(x) ? cos(x)
what is the derivative of x ? 1
so, we have as result :
-4cos(x) + 9