Solve 42x^4y^-3/28x^-2y^4=

$$\frac { 42 x ^ { 4 } y ^ { - 3 } } { 28 x ^ { - 2 } y ^ { 4 } } =$$

Evaluate

$$\frac{3x^{6}}{2y^{7}}$$

Solution Steps

Cancel out 14 in both numerator and denominator.

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

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

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

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

$$\frac{3x^{6}}{2y^{7}}$$

Differentiate w.r.t. x

$$\frac{9x^{5}}{y^{7}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{42}{y^{3}\times 28y^{4}}x^{4-\left(-2\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{2y^{7}}x^{6})$$

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}.

$$6\times \frac{3}{2y^{7}}x^{6-1}$$

Do the arithmetic.

$$\frac{9}{y^{7}}x^{5}$$