Question

question 6 · 1 point
find $\frac{d}{dx}(-4x^{\frac{1}{4}} - 5x^{-\frac{3}{4}})$.
provide your answer below:
$\frac{d}{dx}(-4x^{\frac{1}{4}} - 5x^{-\frac{3}{4}})=$

Explanation:

Step1: Apply power - rule for differentiation

The power - rule states that if $y = ax^n$, then $\frac{dy}{dx}=anx^{n - 1}$. For the function $y=-4x^{\frac{1}{4}}-5x^{-\frac{3}{4}}$, we differentiate each term separately.
For the first term $y_1=-4x^{\frac{1}{4}}$, using the power - rule: $\frac{d}{dx}(-4x^{\frac{1}{4}})=-4\times\frac{1}{4}x^{\frac{1}{4}-1}=-x^{-\frac{3}{4}}$.
For the second term $y_2=-5x^{-\frac{3}{4}}$, using the power - rule: $\frac{d}{dx}(-5x^{-\frac{3}{4}})=-5\times(-\frac{3}{4})x^{-\frac{3}{4}-1}=\frac{15}{4}x^{-\frac{7}{4}}$.

Step2: Combine the derivatives of the terms

$\frac{d}{dx}(-4x^{\frac{1}{4}}-5x^{-\frac{3}{4}})=\frac{d}{dx}(-4x^{\frac{1}{4}})+\frac{d}{dx}(-5x^{-\frac{3}{4}})=-x^{-\frac{3}{4}}+\frac{15}{4}x^{-\frac{7}{4}}$

Answer:

$-x^{-\frac{3}{4}}+\frac{15}{4}x^{-\frac{7}{4}}$