find-the-derivative-of-the-given-function-by-using-logarithmic-differentiation-o

Question

Find the derivative of the given function by using logarithmic differentiation or by using the property $b^{x} = e^{x \ln b}$ .

$y = {(7 x^{2} + 5)}^{x}$

Accepted Answer

$\frac{d y}{d x}=\left(7 x^2+5\right)^x\left(\ln \left(7 x^2+5\right)+\frac{14 x^2}{7 x^2+5}\right)$

Answer

$\frac{d y}{d x} = {(7 x^{2} + 5)}^{x} (\ln (7 x^{2} + 5) - \frac{14 x^{2}}{7 x^{2} + 5})$

Answer

$\frac{d y}{d x} = {(7 x^{2} + 5)}^{x} (\ln (7 x^{2} + 5) - \frac{14 x^{2}}{7 x^{2} + 5})$

Answer

$\frac{d y}{d x} = {(7 x^{2} + 5)}^{x} (\ln (7 x^{2} + 5) - \frac{14 x^{2}}{7 x^{2} + 5})$

Find the derivative of the given function by using logarithmic differentiation or by using the property bx=exlnbb^{x}=e^{x\ln b}.y=(7x2+5)xy=\left(7x^2+5\right)^{x}