The correct answer is the following:
cos x times abs. value sin x
quantity divided by sin x
But see my web site where this is stated much more clearly. There are also graphs to illustrate the problem. See related link below for website.
The derivative of the natural log is 1/x, therefore the derivative is 1/cos(x). However, since the value of cos(x) is submitted within the natural log we must use the chain rule. Then, we multiply 1/cos(x) by the derivative of cos(x). We get the answer: -sin(x)/cos(x) which can be simplified into -tan(x).
There is no real significance to sine plus cosine, now sin2(x) + cos2(x) = 1 for any x, where sin2(x) means to take the sign of the number, then square that value.
f(x) = Cos(x) f'(x) = -Sin(x) Conversely f(x) = Sin(x) f'(x) = Cos(x) NB Note the change of signs.
The derivative of ln x is 1/x The derivative of 2ln x is 2(1/x) = 2/x
If x is a function of time, t, then the second derivative of x, with respect to t, is the acceleration in the x direction.
It is x|x|/2 + C
The function is called the signum function, or sign(x). It is equal to abs(x)/x
The derivative of sin (x) is cos (x). It does not work the other way around, though. The derivative of cos (x) is -sin (x).
The deriviative of sine(x) is cosine(x).
The anti-derivative of 1/x is ln|x| + C, where ln refers to logarithm of x to the base e and |x| refers to the absolute value of x, and C is a constant.
The absolute value of x, |x|, is defined as |x| = x, x>=0; -x, x<0. If you derive this, then you will find that the derivative is 1 when x>=0, and -1 when x<0. But this means that the derivative as x approaches 0 from the left does not equal the derivative as x approaches 0 from the right, as -1=/=1. So the limit as x approaches 0 does not exist, and therefore the gradient does not exist at that point, and so |x| cannot be differentiated at x = 0.
The absolute value of 19 is 19. If x is positive , absolute x equals x.
zero. The absolute value of a number is just the positive version of that number, so the absolute value of x is x, and x minus x is zero.
The derivative of 10x is 10. This is irrespective of the value of x.
If f(x)=1/x then F(x)=antiderivative of f(x)=ln(|x|) (the natural log of the absolute value of x) There's another way of reading this question. The anti derivative of 1 is x+c. Dividing that by x gives you 1 + c/x
I am assuming the you are talking about the graph of the derivative. The graph of the derivative of F(x) is the graph such that, for any x, the value of x on the graph of the derivative of F(x) is the slope at point x in F(x).
The sine of 180 degrees is 0. Remember, the sine value on a unit circle is the y-value. If you find f(pi) in the function f(x)=sin(x), you will get zero as an answer.