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How to use it?
- Derivative of:
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Derivative of x^2*e^2
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Derivative of 3^-x
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Derivative of e^(x*(-4))
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Derivative of (3x-5)^3
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Identical expressions
- (((5x^ three)-2x)^(cosx))
- (((5x cubed ) minus 2x) to the power of ( co sinus of e of x))
- (((5x to the power of three) minus 2x) to the power of ( co sinus of e of x))
- (((5x3)-2x)(cosx))
- 5x3-2xcosx
- (((5x³)-2x)^(cosx))
- (((5x to the power of 3)-2x) to the power of (cosx))
- 5x^3-2x^cosx
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Similar expressions
- (((5x^3)+2x)^(cosx))
Derivative of (((5x^3)-2x)^(cosx))
The solution
You have entered
[src]
cos(x) / 3 \ \5*x - 2*x/
$$\left(5 x^{3} - 2 x\right)^{\cos{\left(x \right)}}$$
(5*x^3 - 2*x)^cos(x)
Detail solution
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Don't know the steps in finding this derivative.
But the derivative is
The answer is:
The first derivative
[src]
cos(x) / / 2\ \
/ 3 \ | / 3 \ \-2 + 15*x /*cos(x)|
\5*x - 2*x/ *|- log\5*x - 2*x/*sin(x) + -------------------|
| 3 |
\ 5*x - 2*x /
$$\left(5 x^{3} - 2 x\right)^{\cos{\left(x \right)}} \left(\frac{\left(15 x^{2} - 2\right) \cos{\left(x \right)}}{5 x^{3} - 2 x} - \log{\left(5 x^{3} - 2 x \right)} \sin{\left(x \right)}\right)$$
The second derivative
[src]
/ 2 2 \
cos(x) |/ / 2\ \ / 2\ / 2\ |
/ / 2\\ || / / 2\\ \-2 + 15*x /*cos(x)| / / 2\\ 30*cos(x) \-2 + 15*x / *cos(x) 2*\-2 + 15*x /*sin(x)|
\x*\-2 + 5*x // *||- log\x*\-2 + 5*x //*sin(x) + -------------------| - cos(x)*log\x*\-2 + 5*x // + --------- - -------------------- - ---------------------|
|| / 2\ | 2 2 / 2\ |
|\ x*\-2 + 5*x / / -2 + 5*x 2 / 2\ x*\-2 + 5*x / |
\ x *\-2 + 5*x / /
$$\left(x \left(5 x^{2} - 2\right)\right)^{\cos{\left(x \right)}} \left(\left(- \log{\left(x \left(5 x^{2} - 2\right) \right)} \sin{\left(x \right)} + \frac{\left(15 x^{2} - 2\right) \cos{\left(x \right)}}{x \left(5 x^{2} - 2\right)}\right)^{2} - \log{\left(x \left(5 x^{2} - 2\right) \right)} \cos{\left(x \right)} + \frac{30 \cos{\left(x \right)}}{5 x^{2} - 2} - \frac{2 \left(15 x^{2} - 2\right) \sin{\left(x \right)}}{x \left(5 x^{2} - 2\right)} - \frac{\left(15 x^{2} - 2\right)^{2} \cos{\left(x \right)}}{x^{2} \left(5 x^{2} - 2\right)^{2}}\right)$$
The third derivative
[src]
/ 3 / 2 \ 3 2 \
cos(x) |/ / 2\ \ / / 2\ \ | / 2\ / 2\ | / 2\ / 2\ / 2\ / 2\ |
/ / 2\\ || / / 2\\ \-2 + 15*x /*cos(x)| / / 2\\ 90*sin(x) | / / 2\\ \-2 + 15*x /*cos(x)| | / / 2\\ 30*cos(x) \-2 + 15*x / *cos(x) 2*\-2 + 15*x /*sin(x)| 30*cos(x) 90*\-2 + 15*x /*cos(x) 3*\-2 + 15*x /*cos(x) 2*\-2 + 15*x / *cos(x) 3*\-2 + 15*x / *sin(x)|
\x*\-2 + 5*x // *||- log\x*\-2 + 5*x //*sin(x) + -------------------| + log\x*\-2 + 5*x //*sin(x) - --------- - 3*|- log\x*\-2 + 5*x //*sin(x) + -------------------|*|cos(x)*log\x*\-2 + 5*x // - --------- + -------------------- + ---------------------| + ------------- - ---------------------- - --------------------- + ---------------------- + ----------------------|
|| / 2\ | 2 | / 2\ | | 2 2 / 2\ | / 2\ 2 / 2\ 3 2 |
|\ x*\-2 + 5*x / / -2 + 5*x \ x*\-2 + 5*x / / | -2 + 5*x 2 / 2\ x*\-2 + 5*x / | x*\-2 + 5*x / / 2\ x*\-2 + 5*x / 3 / 2\ 2 / 2\ |
\ \ x *\-2 + 5*x / / x*\-2 + 5*x / x *\-2 + 5*x / x *\-2 + 5*x / /
$$\left(x \left(5 x^{2} - 2\right)\right)^{\cos{\left(x \right)}} \left(\left(- \log{\left(x \left(5 x^{2} - 2\right) \right)} \sin{\left(x \right)} + \frac{\left(15 x^{2} - 2\right) \cos{\left(x \right)}}{x \left(5 x^{2} - 2\right)}\right)^{3} - 3 \left(- \log{\left(x \left(5 x^{2} - 2\right) \right)} \sin{\left(x \right)} + \frac{\left(15 x^{2} - 2\right) \cos{\left(x \right)}}{x \left(5 x^{2} - 2\right)}\right) \left(\log{\left(x \left(5 x^{2} - 2\right) \right)} \cos{\left(x \right)} - \frac{30 \cos{\left(x \right)}}{5 x^{2} - 2} + \frac{2 \left(15 x^{2} - 2\right) \sin{\left(x \right)}}{x \left(5 x^{2} - 2\right)} + \frac{\left(15 x^{2} - 2\right)^{2} \cos{\left(x \right)}}{x^{2} \left(5 x^{2} - 2\right)^{2}}\right) + \log{\left(x \left(5 x^{2} - 2\right) \right)} \sin{\left(x \right)} - \frac{90 \sin{\left(x \right)}}{5 x^{2} - 2} - \frac{3 \left(15 x^{2} - 2\right) \cos{\left(x \right)}}{x \left(5 x^{2} - 2\right)} + \frac{30 \cos{\left(x \right)}}{x \left(5 x^{2} - 2\right)} - \frac{90 \left(15 x^{2} - 2\right) \cos{\left(x \right)}}{x \left(5 x^{2} - 2\right)^{2}} + \frac{3 \left(15 x^{2} - 2\right)^{2} \sin{\left(x \right)}}{x^{2} \left(5 x^{2} - 2\right)^{2}} + \frac{2 \left(15 x^{2} - 2\right)^{3} \cos{\left(x \right)}}{x^{3} \left(5 x^{2} - 2\right)^{3}}\right)$$