Question

Differentiate the function. g(t)=In(t² +1)⁶ √[7] / {4 t-1}

Answer 1

To differentiate the given function, g(t) = ln(t² + 1)⁶ √7 / (4t - 1), we can apply the rules of differentiation. By using the chain rule and the quotient rule, we can find the derivative of g(t) step by step.

Step-by-step explanation:

To differentiate the function g(t) = ln(t² + 1)⁶ √7 / (4t - 1), we can use the rules of differentiation. Let's break down the steps:

1. Apply the chain rule to differentiate the natural logarithm function, which is ln(x). The derivative of ln(u) with respect to u is 1/u. So, differentiate ln(t² + 1) to get 2t / (t² + 1).
2. The derivative of t⁶ is 6t⁵.
3. The derivative of √7 is 0 because it's a constant.
4. Apply the quotient rule to differentiate the function 1 / (4t - 1). The derivative of 1/u with respect to u is -1/u². So, differentiate 1 / (4t - 1) to get -4 / (4t - 1)².

Putting it all together, the derivative of g(t) is:

g'(t) = (2t / (t² + 1)) * t⁶ * (0) / (4t - 1) - 6t⁵ * ln(t² + 1) * √7 / (4t - 1)²