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- Derivative of a implicit defined function
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- Partial derivative of the function
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How to use it?
- Derivative of:
- Derivative of x^x^x
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Derivative of x^-11
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Derivative of (x+5)/(x+1)
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Derivative of x^(4/3)
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Identical expressions
- x(asin4x+bcos4x)
- x( arc sinus of e of 4x plus b co sinus of e of 4x)
- xasin4x+bcos4x
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Similar expressions
- x(asin4x-bcos4x)
- e^(2x)(asin(4x)+bcos(4x))
- e–x*(a*sin(4*x)+b*cos(4*x))
Derivative of x(asin4x+bcos4x)
The solution
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x*(asin(4*x) + b*cos(4*x))
$$x \left(b \cos{\left(4 x \right)} + \operatorname{asin}{\left(4 x \right)}\right)$$
x*(asin(4*x) + b*cos(4*x))
The first derivative
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/ 4 \
b*cos(4*x) + x*|-------------- - 4*b*sin(4*x)| + asin(4*x)
| ___________ |
| / 2 |
\\/ 1 - 16*x /
$$b \cos{\left(4 x \right)} + x \left(- 4 b \sin{\left(4 x \right)} + \frac{4}{\sqrt{1 - 16 x^{2}}}\right) + \operatorname{asin}{\left(4 x \right)}$$
The second derivative
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/ 1 / 4*x \\ 8*|-------------- - b*sin(4*x) - 2*x*|b*cos(4*x) - --------------|| | ___________ | 3/2|| | / 2 | / 2\ || \\/ 1 - 16*x \ \1 - 16*x / //
$$8 \left(- b \sin{\left(4 x \right)} - 2 x \left(b \cos{\left(4 x \right)} - \frac{4 x}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}}\right) + \frac{1}{\sqrt{1 - 16 x^{2}}}\right)$$
The third derivative
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/ / 2 \ \ | | 1 48*x | 12*x | 16*|-3*b*cos(4*x) + 4*x*|-------------- + b*sin(4*x) + --------------| + --------------| | | 3/2 5/2| 3/2| | |/ 2\ / 2\ | / 2\ | \ \\1 - 16*x / \1 - 16*x / / \1 - 16*x / /
$$16 \left(- 3 b \cos{\left(4 x \right)} + 4 x \left(b \sin{\left(4 x \right)} + \frac{48 x^{2}}{\left(1 - 16 x^{2}\right)^{\frac{5}{2}}} + \frac{1}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}}\right) + \frac{12 x}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}}\right)$$