Question

Find the derivative of the function.y = (tan−1(5x))2.

Answer 1

To find the derivative of the function y = (tan-1(5x))^2, we can use the chain rule and power rule. The derivative of tan-1(5x) is 5/(1+25x^2), and the derivative of y = (tan-1(5x))^2 is 2(tan-1(5x)) * (5/(1+25x^2)).

Step-by-step explanation:

To find the derivative of the function y = (tan-1(5x))2, we can use the chain rule.

Let's start by using the chain rule to find the derivative of tan-1(5x):

1. Let u = 5x.
2. Differentiate both sides with respect to x to get du/dx = 5.
3. Using the chain rule, the derivative of tan-1(5x) is (1/1+u2) * du/dx.
4. Now, substitute u = 5x and du/dx = 5 into the derivative expression.

After simplifying the expression, we get the derivative of tan-1(5x) as 5/(1+25x2). To find the derivative of y = (tan-1(5x))2, we can use the power rule, which states that the derivative of a function raised to a power is equal to the power times the derivative of the function. Therefore, the derivative of y = (tan-1(5x))2 is 2(tan-1(5x)) * (5/(1+25x2)).