Mister Exam
Other calculators
- 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 x^2*cos(x)
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Derivative of x^2*e^(-x)
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Derivative of sin(sqrt(x))
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Derivative of ln(1+x^2)
- Integral of d{x}:
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sin(sqrt(x))
- Limit of the function:
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sin(sqrt(x))
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Identical expressions
- sin(sqrt(x))
- sinus of ( square root of (x))
- sin(√(x))
- sinsqrtx
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Similar expressions
- (6*arcsin(sqrt(x)/2))-((6+x)/2)
- ctg^3(4x)*arcsin(sqrtx)
- log(3)*arcsin(sqrt(x)/(x-5))
- arcsin(sqrt(x/(x+1)))
Derivative of sin(sqrt(x))
The solution
Detail solution
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Let .
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The derivative of sine is cosine:
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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]
/ ___\
cos\\/ x /
----------
___
2*\/ x
$$\frac{\cos{\left(\sqrt{x} \right)}}{2 \sqrt{x}}$$
The second derivative
[src]
/ / ___\ / ___\\
|sin\\/ x / cos\\/ x /|
-|---------- + ----------|
| x 3/2 |
\ x /
---------------------------
4
$$- \frac{\frac{\sin{\left(\sqrt{x} \right)}}{x} + \frac{\cos{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}}}}{4}$$
The third derivative
[src]
/ ___\ / ___\ / ___\
cos\\/ x / 3*sin\\/ x / 3*cos\\/ x /
- ---------- + ------------ + ------------
3/2 2 5/2
x x x
------------------------------------------
8
$$\frac{\frac{3 \sin{\left(\sqrt{x} \right)}}{x^{2}} - \frac{\cos{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}}} + \frac{3 \cos{\left(\sqrt{x} \right)}}{x^{\frac{5}{2}}}}{8}$$
The graph