Solve 12x^8y^-2/4x^5y^-3

$$\frac { 12 x ^ { 8 } y ^ { - 2 } } { 4 x ^ { 5 } y ^ { - 3 } }$$

Evaluate

$$3yx^{3}$$

Solution Steps

Cancel out 4x^{5} in both numerator and denominator.

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

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

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

Calculate y to the power of 1 and get y.

$$3yx^{3}$$

Differentiate w.r.t. x

$$9yx^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{12}{y^{2}\times \frac{4}{y^{3}}}x^{8-5})$$

Do the arithmetic.

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

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}.

$$3\times 3yx^{3-1}$$

Do the arithmetic.

$$9yx^{2}$$