Solve 15x^4z^0y^-2/-3x^6

$$\frac { 15 x ^ { 4 } z ^ { 0 } y ^ { - 2 } } { - 3 x ^ { 6 } }$$

Evaluate

$$-\frac{5}{\left(xy\right)^{2}}$$

Solution Steps

Cancel out 3x^{4} in both numerator and denominator.

$$\frac{5y^{-2}z^{0}}{-x^{2}}$$

Calculate z to the power of 0 and get 1.

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

Multiply 5 and 1 to get 5.

$$\frac{5y^{-2}}{-x^{2}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{-5y^{-2}}{x^{2}}$$

Differentiate w.r.t. x

$$\frac{10}{y^{2}x^{3}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{15z^{0}}{-3y^{2}}x^{4-6})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{5}{y^{2}}\right)x^{-2})$$

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}.

$$-2\left(-\frac{5}{y^{2}}\right)x^{-2-1}$$

Do the arithmetic.

$$\frac{10}{y^{2}}x^{-3}$$