Use the properties of logarithms to find dy/dx for `y=ln((4*e^(3x))/(x^4*sinx))`

1 Answer | Add Yours

Top Answer

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The function `y=ln((4e^(3x))/(x^4*sinx))`

`y=ln((4e^(3x))/(x^4*sinx))`

=> `y = ln(4*e^(3x)) - ln(x^4*sin x)`

=> `y = ln 4 + ln(e^(3x)) - ln x^4 - ln sin x`

=> `y = ln 4 + 3x - 4*ln x - ln sin x`

`dy/dx = 3 - 4/x - (cos x)/(sin x)`

=> `3 - 4/x - cot x`

The required derivative `dy/dx = 3 - 4/x - cot x`

We’ve answered 318,947 questions. We can answer yours, too.

Ask a question