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### 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. $$\displaystyle h\left( t \right) = \frac{{\sqrt {5t + 8} \,\,\,\sqrt{{1 - 9\cos \left( {4t} \right)}}}}{{\sqrt{{{t^2} + 10t}}}}$$ 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