Solve 14x^6y^2div(-1/4x^3)

$$14 x ^ { 6 } y ^ { 2 } \div ( - \frac { 1 } { 4 } x ^ { 3 } )$$

Evaluate

$$-56y^{2}x^{3}$$

Solution Steps

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

$$\frac{14y^{2}x^{3}}{-\frac{1}{4}}$$

Divide 14y^{2}x^{3} by -\frac{1}{4} by multiplying 14y^{2}x^{3} by the reciprocal of -\frac{1}{4}.

$$\frac{14y^{2}x^{3}\times 4}{-1}$$

Anything divided by -1 gives its opposite.

$$-14y^{2}x^{3}\times 4$$

Multiply -14 and 4 to get -56.

$$-56y^{2}x^{3}$$

Differentiate w.r.t. x

$$-168\left(xy\right)^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{14y^{2}}{-\frac{1}{4}}x^{6-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-56y^{2}\right)x^{3})$$

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}.

$$3\left(-56y^{2}\right)x^{3-1}$$

Do the arithmetic.

$$\left(-168y^{2}\right)x^{2}$$