Solve x^92x^4/x^3

$$\frac { x ^ { 9 } 2 x ^ { 4 } } { x ^ { 3 } }$$

Evaluate

$$2x^{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 9 and 4 to get 13.

$$\frac{x^{13}\times 2}{x^{3}}$$

Cancel out x^{3} in both numerator and denominator.

$$2x^{10}$$

Differentiate w.r.t. x

$$20x^{9}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x^{4}}{1}x^{9-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{4}x^{6})$$

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}.

$$6\times 2x^{4}x^{6-1}$$

Do the arithmetic.

$$12x^{4}x^{5}$$