Mister Exam
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- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
- Integral Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Derivative of:
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Derivative of 5x
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Derivative of 5x^3
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Derivative of x*cos(2*x)
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Derivative of x^2+2x
- Integral of d{x}:
- cosx^1/2
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Identical expressions
- cosx^ one / two
- co sinus of e of x to the power of 1 divide by 2
- co sinus of e of x to the power of one divide by two
- cosx1/2
- cosx^1 divide by 2
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Similar expressions
- y=tg2x*arccos(x)^1/2
Derivative of cosx^1/2
The solution
You have entered
[src]
________ \/ cos(x)
$$\sqrt{\cos{\left(x \right)}}$$
d / ________\ --\\/ cos(x) / dx
$$\frac{d}{d x} \sqrt{\cos{\left(x \right)}}$$
Detail solution
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Let .
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Apply the power rule: goes to
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Then, apply the chain rule. Multiply by :
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The derivative of cosine is negative sine:
The result of the chain rule is:
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The answer is:
The first derivative
[src]
-sin(x)
------------
________
2*\/ cos(x)
$$- \frac{\sin{\left(x \right)}}{2 \sqrt{\cos{\left(x \right)}}}$$
The second derivative
[src]
/ 2 \
| ________ sin (x) |
-|2*\/ cos(x) + ---------|
| 3/2 |
\ cos (x)/
----------------------------
4
$$- \frac{\frac{\sin^{2}{\left(x \right)}}{\cos^{\frac{3}{2}}{\left(x \right)}} + 2 \sqrt{\cos{\left(x \right)}}}{4}$$
The third derivative
[src]
/ 2 \
| 3*sin (x)|
-|2 + ---------|*sin(x)
| 2 |
\ cos (x) /
------------------------
________
8*\/ cos(x)
$$- \frac{\left(\frac{3 \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 2\right) \sin{\left(x \right)}}{8 \sqrt{\cos{\left(x \right)}}}$$
The graph