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- Derivative of a implicit defined function
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How to use it?
- Derivative of:
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Derivative of e^(6*x)
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Derivative of -1/y
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Derivative of sin^2(x^2)
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Derivative of log(1+1/(x^2))
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Identical expressions
- (six *x- eight)^(cos(x))
- (6 multiply by x minus 8) to the power of ( co sinus of e of (x))
- (six multiply by x minus eight) to the power of ( co sinus of e of (x))
- (6*x-8)(cos(x))
- 6*x-8cosx
- (6x-8)^(cos(x))
- (6x-8)(cos(x))
- 6x-8cosx
- 6x-8^cosx
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Similar expressions
- (6*x+8)^(cos(x))
- (6*x-8)^(cosx)
Derivative of (6*x-8)^(cos(x))
The solution
You have entered
[src]
cos(x) (6*x - 8)
$$\left(6 x - 8\right)^{\cos{\left(x \right)}}$$
(6*x - 8)^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) / 6*cos(x)\
(6*x - 8) *|-log(6*x - 8)*sin(x) + --------|
\ 6*x - 8 /
$$\left(6 x - 8\right)^{\cos{\left(x \right)}} \left(- \log{\left(6 x - 8 \right)} \sin{\left(x \right)} + \frac{6 \cos{\left(x \right)}}{6 x - 8}\right)$$
The second derivative
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/ 2 \
cos(x) |/ 3*cos(x)\ 9*cos(x) 6*sin(x)|
(2*(-4 + 3*x)) *||log(2*(-4 + 3*x))*sin(x) - --------| - cos(x)*log(2*(-4 + 3*x)) - ----------- - --------|
|\ -4 + 3*x/ 2 -4 + 3*x|
\ (-4 + 3*x) /
$$\left(2 \left(3 x - 4\right)\right)^{\cos{\left(x \right)}} \left(\left(\log{\left(2 \left(3 x - 4\right) \right)} \sin{\left(x \right)} - \frac{3 \cos{\left(x \right)}}{3 x - 4}\right)^{2} - \log{\left(2 \left(3 x - 4\right) \right)} \cos{\left(x \right)} - \frac{6 \sin{\left(x \right)}}{3 x - 4} - \frac{9 \cos{\left(x \right)}}{\left(3 x - 4\right)^{2}}\right)$$
The third derivative
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/ 3 \
cos(x) | / 3*cos(x)\ 9*cos(x) / 3*cos(x)\ / 6*sin(x) 9*cos(x) \ 27*sin(x) 54*cos(x) |
(2*(-4 + 3*x)) *|- |log(2*(-4 + 3*x))*sin(x) - --------| + log(2*(-4 + 3*x))*sin(x) - -------- + 3*|log(2*(-4 + 3*x))*sin(x) - --------|*|cos(x)*log(2*(-4 + 3*x)) + -------- + -----------| + ----------- + -----------|
| \ -4 + 3*x/ -4 + 3*x \ -4 + 3*x/ | -4 + 3*x 2| 2 3|
\ \ (-4 + 3*x) / (-4 + 3*x) (-4 + 3*x) /
$$\left(2 \left(3 x - 4\right)\right)^{\cos{\left(x \right)}} \left(- \left(\log{\left(2 \left(3 x - 4\right) \right)} \sin{\left(x \right)} - \frac{3 \cos{\left(x \right)}}{3 x - 4}\right)^{3} + 3 \left(\log{\left(2 \left(3 x - 4\right) \right)} \sin{\left(x \right)} - \frac{3 \cos{\left(x \right)}}{3 x - 4}\right) \left(\log{\left(2 \left(3 x - 4\right) \right)} \cos{\left(x \right)} + \frac{6 \sin{\left(x \right)}}{3 x - 4} + \frac{9 \cos{\left(x \right)}}{\left(3 x - 4\right)^{2}}\right) + \log{\left(2 \left(3 x - 4\right) \right)} \sin{\left(x \right)} - \frac{9 \cos{\left(x \right)}}{3 x - 4} + \frac{27 \sin{\left(x \right)}}{\left(3 x - 4\right)^{2}} + \frac{54 \cos{\left(x \right)}}{\left(3 x - 4\right)^{3}}\right)$$