Solve 3xy^-1z^-1/4x^-3yz^4

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

Evaluate

$$\frac{3x^{4}}{4y^{2}z^{5}}$$

Solution Steps

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

$$\frac{3\times \frac{1}{y}\times \frac{1}{z}x^{4}}{4yz^{4}}$$

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

$$\frac{3x^{4}}{4y^{2}z^{5}}$$

Differentiate w.r.t. x

$$\frac{3x^{3}}{y^{2}z^{5}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{yz\times 4yz^{4}}x^{1-\left(-3\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{4y^{2}z^{5}}x^{4})$$

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}.

$$4\times \frac{3}{4y^{2}z^{5}}x^{4-1}$$

Do the arithmetic.

$$\frac{3}{y^{2}z^{5}}x^{3}$$