Question

1.Use logarithmic differentiation to find the derivative of the

following function
2. Use logarithmic differentiation to find the derivative of the following function. \[ f(x)=\frac{(3 x+1)^{x} \sqrt{5 x+2}}{\arccos (x) \sin (4 x-5)} \]

Answer 1

The derivative of the function f(x) can be found using logarithmic differentiation, which involves taking the natural logarithm of both sides, using logarithmic properties to expand, differentiating, and then solving for f'(x).

Step-by-step explanation:

To find the derivative of the function f(x)=\frac{(3x+1)^{x} \sqrt{5x+2}}{\arccos (x) \sin (4x-5)} using logarithmic differentiation, we first take the natural logarithm of both sides of the equation to separate the components of the function.

Steps for logarithmic differentiation:

Remember to use the rules that the logarithm of a product is the sum of the logarithms, the logarithm of a quotient is the difference of the logarithms, and the logarithm of a power is the product of the exponent and the logarithm.