Derivative of y=ln|2-x-5x^2|: 1+10x/-2+x+5x^2

• 2slowtogofast
In summary, the derivative of y=ln|2-x-5x^2| is -10x/(2-x-5x^2) + (1+10x)/(2+x+5x^2). To find the derivative of a natural logarithm function, you use the rule: d/dx ln(u) = 1/u * du/dx. The chain rule is a method for finding the derivative of a composite function. It can be simplified to -10x/(2-x-5x^2) + 1/(2-x-5x^2). The derivative of a logarithm function has applications in physics, economics, and biology.
2slowtogofast
y = ln|2-x-5x^2|

when you take the derivitve of somthing like this you can ignore the abs value signs right?

for the ans i got -1-10x / 2-x-5x^2
the answer is 1+10x / -2+x+5x^2

i obviously made some mistake some where because i have the same number just with different signs

The two answers are the same. If the first answer is given by $-a/b[/tex], the second one would be [itex]a/-b$. The negative is just in a different place.

thanks i didt see that

1. What is the derivative of y=ln|2-x-5x^2|: 1+10x/-2+x+5x^2?

The derivative of y=ln|2-x-5x^2|: 1+10x/-2+x+5x^2 is -10x/(2-x-5x^2) + (1+10x)/(2+x+5x^2).

2. How do you find the derivative of a natural logarithm function?

To find the derivative of a natural logarithm function, you use the rule: d/dx ln(u) = 1/u * du/dx. In this case, let u=2-x-5x^2, and use the chain rule to find du/dx.

3. What is the chain rule?

The chain rule is a method for finding the derivative of a composite function. It states that if y=f(g(x)), then dy/dx = f'(g(x)) * g'(x).

4. Can you simplify the derivative of y=ln|2-x-5x^2|: 1+10x/-2+x+5x^2?

Yes, the derivative can be simplified to -10x/(2-x-5x^2) + 1/(2-x-5x^2).

5. How can the derivative of a logarithm function be applied in real life?

The derivative of a logarithm function can be applied in various fields such as physics, economics, and biology. For example, in physics, the derivative of a logarithmic function can be used to calculate the rate of change of a physical quantity over time. In economics, it can be used to determine the marginal cost or revenue of a product. In biology, it can be used to model population growth or decay.

Replies
4
Views
2K
Replies
11
Views
1K
Replies
5
Views
2K
Replies
11
Views
2K
Replies
4
Views
4K
Replies
3
Views
2K
Replies
6
Views
1K
Replies
18
Views
3K
Replies
6
Views
2K
Replies
6
Views
1K