Derivatives · Wed, Nov 4, 2026

Answer: $-30x^{5} + 64x^{7} + 5$

1. Apply the power rule to each term: bring down the exponent and subtract 1 from it. A constant has derivative 0.

   $$\frac{d}{dx}\left(a x^n\right) = a n x^{n-1}$$

2. Differentiate this term.

   $$\frac{d}{dx}\left(-5x^{6}\right) = -30x^{5}$$

3. Differentiate this term.

   $$\frac{d}{dx}\left(5x\right) = 5$$

4. Differentiate this term.

   $$\frac{d}{dx}\left(8x^{8}\right) = 64x^{7}$$

5. So the answer is

   $$\frac{d}{dx}\left(-5x^{6} + 5x + 8x^{8}\right) = -30x^{5} + 64x^{7} + 5$$