Solve 2x^2*6x/3x^4

$$\frac { 2 x ^ { 2 } \times 6 x } { 3 x ^ { 4 } }$$

Evaluate

$$\frac{4}{x}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{2x^{3}\times 6}{3x^{4}}$$

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

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

Multiply 2 and 2 to get 4.

$$\frac{4}{x}$$

Differentiate w.r.t. x

$$-\frac{4}{x^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{12x}{3}x^{2-4})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$\left(-8x\right)x^{-3}$$