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Exercise

$f\left(x\right)=\sqrt{\frac{x^4+lnx}{e^x\:cos^3\:x}}$

Step-by-step Solution

1

Since $\cos$ is the reciprocal of $\sec$, $\frac{x^4+\ln\left(x\right)}{e^x\cos\left(x\right)^3}$ is equivalent to $\frac{\left(x^4+\ln\left(x\right)\right)\sec\left(x\right)^3}{e^x}$

$f\left(x\right)=\sqrt{\frac{\left(x^4+\ln\left(x\right)\right)\sec\left(x\right)^3}{e^x}}$

Final answer to the exercise

$f\left(x\right)=\sqrt{\frac{\left(x^4+\ln\left(x\right)\right)\sec\left(x\right)^3}{e^x}}$

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