Question

find the derivative of $f(x) = -15sin x + \frac{11}{x^4} + 3sqrt7{x} - 5$.

$\circ$ $f(x) = -15cos x - \frac{44}{x^5} + \frac{3}{7x^{\frac{6}{7}}}$

$\circ$ $f(x) = 15cos x - \frac{44}{x^5} + \frac{3}{7x^{\frac{6}{7}}}$

$\circ$ $f(x) = -15cos x + \frac{11}{4x^3} + \frac{3}{7x^{\frac{6}{7}}} - 5$

$\circ$ $f(x) = 15cos x + \frac{11}{4x^3} + \frac{3}{7x^{\frac{6}{7}}}$

Explanation:

Step1: Rewrite function terms

$f(x) = -15\sin x + 11x^{-4} + 3x^{\frac{1}{7}} - 5$

Step2: Differentiate term by term

• Derivative of $-15\sin x$: $-15\cos x$
• Derivative of $11x^{-4}$: $11\times(-4)x^{-5} = -\frac{44}{x^5}$
• Derivative of $3x^{\frac{1}{7}}$: $3\times\frac{1}{7}x^{\frac{1}{7}-1} = \frac{3}{7x^{\frac{6}{7}}}$
• Derivative of $-5$: $0$

Step3: Combine all derivatives

$f'(x) = -15\cos x - \frac{44}{x^5} + \frac{3}{7x^{\frac{6}{7}}}$

Answer:

A. $f'(x)= - 15\cos x-\frac{44}{x^{5}}+\frac{3}{7x^{\frac{6}{7}}}$