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 4/x^3
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Derivative of x^6/6
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Derivative of x^3/x
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Derivative of (x-3)^4
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Identical expressions
- twenty / three *sin(x)*cos(x)
- 20 divide by 3 multiply by sinus of (x) multiply by co sinus of e of (x)
- twenty divide by three multiply by sinus of (x) multiply by co sinus of e of (x)
- 20/3sin(x)cos(x)
- 20/3sinxcosx
- 20 divide by 3*sin(x)*cos(x)
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Similar expressions
- 20/3*(sin(x)*cos(x))
- 20/3*sinx*cosx
Derivative of 20/3*sin(x)*cos(x)
The solution
You have entered
[src]
20*sin(x)*cos(x)
----------------
3
$$\frac{20 \sin{\left(x \right)} \cos{\left(x \right)}}{3}$$
d /20*sin(x)*cos(x)\ --|----------------| dx\ 3 /
$$\frac{d}{d x} \frac{20 \sin{\left(x \right)} \cos{\left(x \right)}}{3}$$
Detail solution
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The derivative of a constant times a function is the constant times the derivative of the function.
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Apply the product rule:
; to find :
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The derivative of cosine is negative sine:
; to find :
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The derivative of sine is cosine:
The result is:
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So, the result is:
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Now simplify:
The answer is:
The first derivative
[src]
2 2
20*sin (x) 20*cos (x)
- ---------- + ----------
3 3
$$- \frac{20 \sin^{2}{\left(x \right)}}{3} + \frac{20 \cos^{2}{\left(x \right)}}{3}$$
The second derivative
[src]
-80*cos(x)*sin(x)
-----------------
3
$$- \frac{80 \sin{\left(x \right)} \cos{\left(x \right)}}{3}$$
The third derivative
[src]
/ 2 2 \
80*\sin (x) - cos (x)/
----------------------
3
$$\frac{80 \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right)}{3}$$
The graph