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 u
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Derivative of e^x/x^2
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Derivative of cos(x)/x^2
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Derivative of cos(sqrt(x))
- Limit of the function:
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cos(sqrt(x))
- Integral of d{x}:
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cos(sqrt(x))
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Identical expressions
- cos(sqrt(x))
- co sinus of e of ( square root of (x))
- cos(√(x))
- cossqrtx
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Similar expressions
- (arcsin4*x)/(arccos*(sqrtx))
- (x-1)/(x+2)*arccos(sqrt(x-1))
- arccos((sqrt(x))/(1+x))
- y=(x+1)^(arccossqrt(x))
Derivative of cos(sqrt(x))
The solution
You have entered
[src]
/ ___\ cos\\/ x /
$$\cos{\left(\sqrt{x} \right)}$$
d / / ___\\ --\cos\\/ x // dx
$$\frac{d}{d x} \cos{\left(\sqrt{x} \right)}$$
Detail solution
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Let .
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The derivative of cosine is negative sine:
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Then, apply the chain rule. Multiply by :
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Apply the power rule: goes to
The result of the chain rule is:
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The answer is:
The first derivative
[src]
/ ___\
-sin\\/ x /
------------
___
2*\/ x
$$- \frac{\sin{\left(\sqrt{x} \right)}}{2 \sqrt{x}}$$
The second derivative
[src]
/ ___\ / ___\
sin\\/ x / cos\\/ x /
---------- - ----------
3/2 x
x
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4
$$\frac{- \frac{\cos{\left(\sqrt{x} \right)}}{x} + \frac{\sin{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}}}}{4}$$
The third derivative
[src]
/ ___\ / ___\ / ___\
sin\\/ x / 3*sin\\/ x / 3*cos\\/ x /
---------- - ------------ + ------------
3/2 5/2 2
x x x
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8
$$\frac{\frac{3 \cos{\left(\sqrt{x} \right)}}{x^{2}} + \frac{\sin{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}}} - \frac{3 \sin{\left(\sqrt{x} \right)}}{x^{\frac{5}{2}}}}{8}$$
The graph