find the derivative of the following function. f(x)=6x^4 - 37x + e^5 f(x)=□

Answer:

$24x^{3}-37$

Explanation:

Step1: Apply power - rule to $6x^{4}$

$\frac{d}{dx}(6x^{4})=6\times4x^{4 - 1}=24x^{3}$

Step2: Apply power - rule to $-37x$

$\frac{d}{dx}(-37x)=-37\times1x^{1 - 1}=-37$

Step3: Differentiate the constant $e^{5}$

$\frac{d}{dx}(e^{5}) = 0$ (since the derivative of a constant is 0)

Step4: Combine the results

$f'(x)=\frac{d}{dx}(6x^{4})+\frac{d}{dx}(-37x)+\frac{d}{dx}(e^{5})=24x^{3}-37+0 = 24x^{3}-37$