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To find the derivatve of the square root of cos x:
Use the chain rule; this means multiply the inner derivative by the outer derivative.
You can write the question f(x) = (cos x)1/2
This general break-down explains how to find d/dx f(x)
note: d/dx basically symbolizes "the derivative of"
In general terms:
f(x) = x1/2
g(x) = cos x
f(g(x)) = (cos x)1/2
outer derivative: d/dx f(z) = (1/2)*x-1/2 = 1/(4cos x)1/2
inner derivative: d/dx g(x) = -sin(x)
final answer: d/dx f(g(x)) = -sin(x)/(4*cos x)1/2
note: d/dx means "the derivative of"; so d/dx x = 1
Further explained:
Set up the equation to a more general form: (cos x)1/2
To make the inner derivative, look at cos(x)
To make the outer derivative, look at x1/2
note: x ~ cos x; so we treat (cos x) simply as x, to create the outer derivative
You probably know the necessary derivates:
1. derivative of cos x = -sin x
2. derivative of a1/2 = (1/2)*a-1/2 = 1/(4a)1/2
Multiplying the two we get the answer:
-sin(x)/(4cos x)1/2
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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 square root 2 sin x?
It is not totally clear to what the square root applies*; if just the 2, then: d/dx ((√2)sin x) = (√2) cos x if all of 2 sin x, then: d/dx (√(2 sin x)) = cos x / √(2 sin x) * for the second version I would expect "square root all of 2 sin x" but some people would write as given in the question meaning this, so I've given both just in case.
What is integral square root of sin x.dx?
-cos(x) + constant
What is the value of cos pie4?
cos pi over four equals the square root of 2 over 2 This value can be found by looking at a unit circle. Cos indicates it is the x value of the point pi/4 which is (square root 2 over 2, square root 2 over 2)
Find y'' if y equals 6x sinx?
That means you must take the derivative of the derivative. In this case, you must use the product rule. y = 6x sin x y'= 6[x (sin x)' + (x)' sin x] = 6[x cos x + sin x] y'' = 6[x (cos x)' + (x)' cos x + cos x] = 6[x (-sin x) + cos x + cos x] = 6[-x sin x + 2 cos x]
How do you differentiate cosine square root of x?
The derivative of cos x is -sin x, the derivative of square root of x is 1/(2 root(x)). Applying the chain rule, the derivative of cos root(x) is -sin x times 1/(2 root(x)), or - sin x / (2 root x).
How do you get the derivative of a square root?
The square root of x = x to the power of a half
What is the derivative of square root of x-5?
Use the formula for the derivative of a power. The square root of (x-5) is the same as (x-5)1/2.
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 ln cos x?
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).
What is the second derivative of the square root of x to the power of 3?
3/(4*square root(x)) ....Mukesh
What is the derivative of cos x sin x divided by cos x sin x?
(cos x sin x) / (cos x sin x) = 1. The derivative of a constant, such as 1, is zero.
When does cos x equal -sin x?
The derivative of cos(x) equals -sin(x); therefore, the anti-derivative of -sin(x) equals cos(x).
What is the Derivative of sine ex?
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).
What is the derivative of the square root of one minus x squared?
The derivative, with respect to x, is -x/sqrt(1-x2)
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.
