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For f(x) + g(x), the derivative d/dx[f(x) + g(x)] = f'(x) + g'(x). Essentially, this just means that since it's addition, you can take the derivative of each part.
d/dx(x - 2cosx) =
* d/dx is a way to indicate you're taking the derivative
d/dx(x) + d/dx(-2cosx)
* take the derivative of each part, distributing
(1) + (-2*-sinx)
* f(x) = x, f'(x) = 1 & g(x) = -2cosx, g'(x) = +2sinx
= 1 + 2sinx
I'll solve two derivatives for you, because I'm not sure if you meant x squared or 2x.
y = x2cos(x)y` = ?
We need to use the product rule:
If a = x2 and b = cos(x) then:
y` = a`b + ab`
a` = 2x
b` = -sin(x)
y` = (2x)cos(x)-x2sin(x)
y = 2xcos(x)y` = ?
Again we need to use the product rule:
a = 2x, b = cos(x)
a`= 2, b`= -sin(x)
y` = a`b + ab`
y` = 2cos(x)-(2x)sin(x)
Once again, I solved two different problems here, because I was unsure about what problem you were asking about:
[x2cos(x)]` =(2x)cos(x)-x2sin(x)
[2xcos(x)]` =2cos(x)-(2x)sin(x)
Add your answer:
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What is the anti-derivative of -2cosx?
take out the constant -2 then take the intergral of cosx this will give you sinx your answer is -2sinx
What is the derivative of 2lnx?
The derivative of ln x is 1/x The derivative of 2ln x is 2(1/x) = 2/x
What is the derivative of 3cosx?
The derivative of 3cos(x) is -3sin(x). This can be found using the chain rule, which states that the derivative of a composition of functions is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function. In this case, the derivative of cos(x) is -sin(x), and when multiplied by the constant 3, we get -3sin(x) as the derivative of 3cos(x).
What is the derivative of csc x?
The derivative of csc(x) is -cot(x)csc(x).
What is the derivative of sec squared x?
derivative of sec2(x)=2tan(x)sec2(x)
What is the derivative of 2cosx?
d/dx 2 cos x = -2 sin x
What is the derivative of 2 cos x -2 sin x?
4
What is the anti-derivative of -2cosx?
take out the constant -2 then take the intergral of cosx this will give you sinx your answer is -2sinx
What is cos2 x divided by cos x?
cos2x/cosx = 2cosx - 1/cosx
What is the derivative of 2lnx?
The derivative of ln x is 1/x The derivative of 2ln x is 2(1/x) = 2/x
Derivative of cosx?
The derivative of cos(x) is negative sin(x). Also, the derivative of sin(x) is cos(x).
What is the derivative of sinπx?
The derivative with respect to 'x' of sin(pi x) ispi cos(pi x)
What is the derivative of csc x?
The derivative of csc(x) is -cot(x)csc(x).
What is the derivative of secant x?
The derivative of sec(x) is sec(x) tan(x).
What is the derivative of cotx?
The derivative of cot(x) is -csc2(x).
What is the third derivative of lnx?
Oh, dude, the third derivative of ln(x) is -2/(x^3). But like, who really needs to know that, right? I mean, unless you're planning on impressing your calculus teacher or something. Just remember, math is like a puzzle, except no one actually wants to put it together.
What is the second derivitive of sec x?
Write sec x as a function of sines and cosines (in this case, sec x = 1 / cos x). Then use the division formula to take the first derivative. Take the derivative of the first derivative to get the second derivative. Reminder: the derivative of sin x is cos x; the derivative of cos x is - sin x.
