Question

Determinar f'(x), onde f(x) = 5$x^{sec(x)}$

Answer 1

$\boxed{f(x)=5x^{\sec{x}}}$

$\dfrac{\mathrm{d}f}{\mathrm{d}x}=5\dfrac{\mathrm{d}}{\mathrm{d}x}\big(x^{\sec{x}}\big)$

$\dfrac{\mathrm{d}f}{\mathrm{d}x}=5x^{\sec{x}}\dfrac{\mathrm{d}}{\mathrm{d}x}\bigg(\ln{x}\sec{x}\bigg)$

$\dfrac{\mathrm{d}f}{\mathrm{d}x}=5x^{\sec{x}}\bigg(\sec{x}\dfrac{\mathrm{d}}{\mathrm{d}x}(\ln{x})+\ln{x}\dfrac{\mathrm{d}}{\mathrm{d}x}(\sec{x})\bigg)$

$\boxed{\dfrac{\mathrm{d}f}{\mathrm{d}x}=5x^{\sec{x}}\bigg(\dfrac{\sec{x}}{x}+\ln{x}\sec{x}\tan{x}\bigg)}$