find the derivative of the function. y=(tan^-1(7x))^2
To find the derivative of the function y = (tan^-1(7x))^2, we can use the chain rule.
Let's denote u = tan^-1(7x). Therefore, the function becomes y = u^2.
To find the derivative, we can use the chain rule.
dy/du = 2u * du/dx
Now we need to find du/dx. Since u = tan^-1(7x), we can use the derivative rules to find du/dx:
du/dx = d/dx(tan^-1(7x))
Now, using the chain rule again, we can find du/dx:
du/dx = (1/((7x)^2 + 1)) * d/dx(7x))
= (1/((49x^2 + 1)) * 7
= 7/(49x^2 + 1)
Finally, we can substitute the values back into the first equation:
dy/du = 2u * du/dx
= 2(tan^-1(7x)) * (7/(49x^2 + 1))
Therefore, the derivative of the function y = (tan^-1(7x))^2 is 2(tan^-1(7x)) * (7/(49x^2 + 1)).