Solve 6x^3y^4/2x^-1y

$$\frac { 6 x ^ { 3 } y ^ { 4 } } { 2 x ^ { - 1 } y }$$

Evaluate

$$3y^{3}x^{4}$$

Solution Steps

Cancel out 2y in both numerator and denominator.

$$\frac{3x^{3}y^{3}}{\frac{1}{x}}$$

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

$$3y^{3}x^{4}$$

Differentiate w.r.t. x

$$12\left(xy\right)^{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6y^{4}}{2y}x^{3-\left(-1\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3y^{3}x^{4})$$

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}.

$$4\times 3y^{3}x^{4-1}$$

Do the arithmetic.

$$12y^{3}x^{3}$$