The question is
if p(x)= 2x³-3x+5, what is the remainder of p(x) divided by (x-5)
We use the synthetic division to find the remainder,
x-5=0
x=5
Now, write the coefficients of polynomial.
5 | 2 0 -3 5
| ↓ 10 50 235
-------------------------------
2 10 47 | 240→ is the remainder.
Quotient= 2x²+10x+47
Remainder= 240
Specify, what are you needing?
Answer:
![f'(x) = -\frac{2x}{1 - x^{2}}](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20-%5Cfrac%7B2x%7D%7B1%20-%20x%5E%7B2%7D%7D)
Step-by-step explanation:
The derivative of an addition/subtraction of terms is the addition/subtraction of the derivatives of these terms.
The derivative of a constant is 0.
The derivative of
is
. The derivative of
is
, for example.
The derivative of the ln function:
If we have:
![y = \ln{g(x)}](https://tex.z-dn.net/?f=y%20%3D%20%5Cln%7Bg%28x%29%7D)
The derivative is
![y' = g'(x)*\frac{1}{g(x)}](https://tex.z-dn.net/?f=y%27%20%3D%20g%27%28x%29%2A%5Cfrac%7B1%7D%7Bg%28x%29%7D)
In this problem, we have that:
![y = \ln{1 - x^{2}}](https://tex.z-dn.net/?f=y%20%3D%20%5Cln%7B1%20-%20x%5E%7B2%7D%7D)
So
and ![g'(x) = -2x](https://tex.z-dn.net/?f=g%27%28x%29%20%3D%20-2x)
So the derivative to this function is
![f'(x) = -\frac{2x}{1 - x^{2}}](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20-%5Cfrac%7B2x%7D%7B1%20-%20x%5E%7B2%7D%7D)