Solve x^4(2x^4)/x^2

$$\frac { x ^ { 4 } ( 2 x ^ { 4 } ) } { x ^ { 2 } }$$

Evaluate

$$2x^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

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

Cancel out x^{2} in both numerator and denominator.

$$2x^{6}$$

Differentiate w.r.t. x

$$12x^{5}$$

Solution Steps

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

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

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$4x^{4}x^{1}$$

For any term t, t^{1}=t.

$$4x^{4}x$$