Solve x^3*x^5-2x^9:x

$$x ^ { 3 } \cdot x ^ { 5 } - 2 x ^ { 9 } : x$$

Evaluate

$$-x^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$x^{8}-\frac{2x^{9}}{x}$$

Cancel out x in both numerator and denominator.

$$x^{8}-2x^{8}$$

Combine x^{8} and -2x^{8} to get -x^{8}.

$$-x^{8}$$

Differentiate w.r.t. x

$$-8x^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{8}-\frac{2x^{9}}{x})$$

Cancel out x in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{8}-2x^{8})$$

Combine x^{8} and -2x^{8} to get -x^{8}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-x^{8})$$

The derivative of ax^{n} is nax^{n-1}.

$$8\left(-1\right)x^{8-1}$$

Multiply 8 times -1.

$$-8x^{8-1}$$

Subtract 1 from 8.

$$-8x^{7}$$