Show All Notes Hide All Notes

Section 3.13 : Logarithmic Differentiation

For problems 1 – 3 use logarithmic differentiation to find the first derivative of the given function.

1. \(f\left( x \right) = {\left( {5 - 3{x^2}} \right)^7}\,\,\sqrt {6{x^2} + 8x - 12} \) Solution
2. \(\displaystyle y = \frac{{\sin \left( {3z + {z^2}} \right)}}{{{{\left( {6 - {z^4}} \right)}^3}}}\) Solution
3. \(\displaystyle h\left( t \right) = \frac{{\sqrt {5t + 8} \,\,\,\sqrt[3]{{1 - 9\cos \left( {4t} \right)}}}}{{\sqrt[4]{{{t^2} + 10t}}}}\) Solution

For problems 4 & 5 find the first derivative of the given function.

1. \(g\left( w \right) = {\left( {3w - 7} \right)^{4w}}\) Solution
2. \(f\left( x \right) = {\left( {2x - {{\bf{e}}^{8x}}} \right)^{\sin \left( {2x} \right)}}\) Solution