log(x) - 4*cos(x)
Differentiate log(x)−4cos(x)\log{\left(x \right)} - 4 \cos{\left(x \right)}log(x)−4cos(x) term by term:
The derivative of log(x)\log{\left(x \right)}log(x) is 1x\frac{1}{x}x1.
The derivative of a constant times a function is the constant times the derivative of the function.
The derivative of cosine is negative sine:
So, the result is: 4sin(x)4 \sin{\left(x \right)}4sin(x)
The result is: 4sin(x)+1x4 \sin{\left(x \right)} + \frac{1}{x}4sin(x)+x1
The answer is:
1 - + 4*sin(x) x
1 - -- + 4*cos(x) 2 x
/1 \ 2*|-- - 2*sin(x)| | 3 | \x /