Question

Find the derivative of y equals log subscript 6 open parentheses fraction numerator 2 x to the power of 7 over denominator 5 x cubed minus 27 end fraction close parentheses?

Answer 1

To find the derivative, use logarithmic differentiation to transform the equation and then apply the chain and product rule to differentiate.

Step-by-step explanation:

To find the derivative of the given function, we can use logarithmic differentiation. Let me show you the step-by-step process:

1. Start by taking the natural logarithm of both sides of the equation: ln(y) = ln(log6((2x^7)/(5x^3 - 27))).
2. Apply the logarithmic property of the natural logarithm and simplify the expression: ln(y) = (7ln(2x) - ln(5x^3 - 27)) / ln(6).
3. Now, differentiate both sides of the equation with respect to x, using the chain rule and product rule where needed.
4. Solve for dy/dx to find the derivative of y.