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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 (x+4)/(x-1)
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Derivative of x^2-7*x
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Derivative of x^2+4x
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Derivative of lnx^2
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Identical expressions
- y=(x+ one)^(arccossqrt(x))
- y equally (x plus 1) to the power of (arc co sinus of e of square root of (x))
- y equally (x plus one) to the power of (arc co sinus of e of square root of (x))
- y=(x+1)^(arccos√(x))
- y=(x+1)(arccossqrt(x))
- y=x+1arccossqrtx
- y=x+1^arccossqrtx
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Similar expressions
- y=(x-1)^(arccossqrt(x))
Derivative of y=(x+1)^(arccossqrt(x))
The solution
You have entered
[src]
/ ___\
acos\\/ x /
(x + 1)
$$\left(x + 1\right)^{\operatorname{acos}{\left(\sqrt{x} \right)}}$$
(x + 1)^acos(sqrt(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]
/ ___\ / / ___\ \
acos\\/ x / |acos\\/ x / log(x + 1) |
(x + 1) *|----------- - -----------------|
| x + 1 ___ _______|
\ 2*\/ x *\/ 1 - x /
$$\left(x + 1\right)^{\operatorname{acos}{\left(\sqrt{x} \right)}} \left(\frac{\operatorname{acos}{\left(\sqrt{x} \right)}}{x + 1} - \frac{\log{\left(x + 1 \right)}}{2 \sqrt{x} \sqrt{1 - x}}\right)$$
The second derivative
[src]
/ 2 \
|/ / ___\ \ |
||2*acos\\/ x / log(1 + x) | |
||------------- - ---------------| |
/ ___\ || 1 + x ___ _______| / ___\ |
acos\\/ x / |\ \/ x *\/ 1 - x / acos\\/ x / 1 log(1 + x) log(1 + x) |
(1 + x) *|---------------------------------- - ----------- - ----------------------- - ------------------ + ----------------|
| 4 2 ___ _______ ___ 3/2 3/2 _______|
\ (1 + x) \/ x *(1 + x)*\/ 1 - x 4*\/ x *(1 - x) 4*x *\/ 1 - x /
$$\left(x + 1\right)^{\operatorname{acos}{\left(\sqrt{x} \right)}} \left(\frac{\left(\frac{2 \operatorname{acos}{\left(\sqrt{x} \right)}}{x + 1} - \frac{\log{\left(x + 1 \right)}}{\sqrt{x} \sqrt{1 - x}}\right)^{2}}{4} - \frac{\operatorname{acos}{\left(\sqrt{x} \right)}}{\left(x + 1\right)^{2}} - \frac{1}{\sqrt{x} \sqrt{1 - x} \left(x + 1\right)} - \frac{\log{\left(x + 1 \right)}}{4 \sqrt{x} \left(1 - x\right)^{\frac{3}{2}}} + \frac{\log{\left(x + 1 \right)}}{4 x^{\frac{3}{2}} \sqrt{1 - x}}\right)$$
The third derivative
[src]
/ 3 \
|/ / ___\ \ / / ___\ \ / / ___\ \ |
||2*acos\\/ x / log(1 + x) | |2*acos\\/ x / log(1 + x) | |4*acos\\/ x / log(1 + x) log(1 + x) 4 | |
||------------- - ---------------| 3*|------------- - ---------------|*|------------- + ---------------- - -------------- + -----------------------| |
/ ___\ || 1 + x ___ _______| / ___\ | 1 + x ___ _______| | 2 ___ 3/2 3/2 _______ ___ _______| |
acos\\/ x / |\ \/ x *\/ 1 - x / 2*acos\\/ x / \ \/ x *\/ 1 - x / \ (1 + x) \/ x *(1 - x) x *\/ 1 - x \/ x *(1 + x)*\/ 1 - x / 3 3*log(1 + x) 3*log(1 + x) log(1 + x) 3 3 |
(1 + x) *|---------------------------------- + ------------- - ----------------------------------------------------------------------------------------------------------------- - -------------------------- - ---------------- - ------------------ + ----------------- + -------------------------- + ------------------------|
| 8 3 8 ___ 3/2 5/2 _______ ___ 5/2 3/2 3/2 ___ 2 _______ 3/2 _______|
\ (1 + x) 4*\/ x *(1 + x)*(1 - x) 8*x *\/ 1 - x 8*\/ x *(1 - x) 4*x *(1 - x) 2*\/ x *(1 + x) *\/ 1 - x 4*x *(1 + x)*\/ 1 - x /
$$\left(x + 1\right)^{\operatorname{acos}{\left(\sqrt{x} \right)}} \left(\frac{\left(\frac{2 \operatorname{acos}{\left(\sqrt{x} \right)}}{x + 1} - \frac{\log{\left(x + 1 \right)}}{\sqrt{x} \sqrt{1 - x}}\right)^{3}}{8} - \frac{3 \left(\frac{2 \operatorname{acos}{\left(\sqrt{x} \right)}}{x + 1} - \frac{\log{\left(x + 1 \right)}}{\sqrt{x} \sqrt{1 - x}}\right) \left(\frac{4 \operatorname{acos}{\left(\sqrt{x} \right)}}{\left(x + 1\right)^{2}} + \frac{4}{\sqrt{x} \sqrt{1 - x} \left(x + 1\right)} + \frac{\log{\left(x + 1 \right)}}{\sqrt{x} \left(1 - x\right)^{\frac{3}{2}}} - \frac{\log{\left(x + 1 \right)}}{x^{\frac{3}{2}} \sqrt{1 - x}}\right)}{8} + \frac{2 \operatorname{acos}{\left(\sqrt{x} \right)}}{\left(x + 1\right)^{3}} + \frac{3}{2 \sqrt{x} \sqrt{1 - x} \left(x + 1\right)^{2}} - \frac{3}{4 \sqrt{x} \left(1 - x\right)^{\frac{3}{2}} \left(x + 1\right)} - \frac{3 \log{\left(x + 1 \right)}}{8 \sqrt{x} \left(1 - x\right)^{\frac{5}{2}}} + \frac{3}{4 x^{\frac{3}{2}} \sqrt{1 - x} \left(x + 1\right)} + \frac{\log{\left(x + 1 \right)}}{4 x^{\frac{3}{2}} \left(1 - x\right)^{\frac{3}{2}}} - \frac{3 \log{\left(x + 1 \right)}}{8 x^{\frac{5}{2}} \sqrt{1 - x}}\right)$$
The graph