Solve (x^5)(x)(x^-3)/x^-4

$$\frac { ( x ^ { 5 } ) ( x ) ( x ^ { - 3 } ) } { x ^ { - 4 } }$$

Evaluate

$$x^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$\frac{x^{6}x^{-3}}{x^{-4}}$$

To multiply powers of the same base, add their exponents. Add 6 and -3 to get 3.

$$\frac{x^{3}}{x^{-4}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -4 from 3 to get 7.

$$x^{7}$$

Differentiate w.r.t. x

$$7x^{6}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{x^{3}}x^{5-\left(-4\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{x^{2}}x^{9})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$9\times \frac{1}{x^{2}}x^{9-1}$$

Do the arithmetic.

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