use logarithmic differentiation to find the derivative of the function.\n\n$y=(x^{5}+2)^{2}(x^{4}+4)^{4}$
use logarithmic differentiation to find the derivative of the function.\n\n$y=(x^{5}+2)^{2}(x^{4}+4)^{4}$
Answer
Explanation:
Step1: Take natural - log of both sides
$\ln y=2\ln(x^{5}+2)+4\ln(x^{4}+4)$
Step2: Differentiate both sides
$\frac{y'}{y}=\frac{2\times5x^{4}}{x^{5}+2}+\frac{4\times4x^{3}}{x^{4}+4}$
Step3: Solve for $y'$
$y'=(x^{5}+2)^{2}(x^{4}+4)^{4}(\frac{10x^{4}}{x^{5}+2}+\frac{16x^{3}}{x^{4}+4})$
Answer:
$y'=(x^{5}+2)^{2}(x^{4}+4)^{4}(\frac{10x^{4}}{x^{5}+2}+\frac{16x^{3}}{x^{4}+4})$