Solve 3x^-4y^-3/x^3

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

Differentiate w.r.t. x

$$-\frac{21}{y^{3}x^{8}}$$

Solution Steps

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

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

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$\left(-\frac{21}{y^{3}}\right)x^{-8}$$

Evaluate

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

Solution Steps

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

$$\frac{3y^{-3}}{x^{7}}$$