Solve 6x^3y^2/10x^4y^2{z^}

$$\frac{ 6 { x }^{ 3 } { y }^{ 2 } }{ 10 { x }^{ 4 } { y }^{ 2 } { z }^{ } }$$

Evaluate

$$\frac{3}{5xz}$$

Solution Steps

Cancel out 2y^{2}x^{3} in both numerator and denominator.

$$\frac{3}{5xz^{1}}$$

Calculate z to the power of 1 and get z.

$$\frac{3}{5xz}$$

Differentiate w.r.t. x

$$-\frac{3}{5zx^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6y^{2}}{10z^{1}y^{2}}x^{3-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{5z}\times \frac{1}{x})$$

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}.

$$-\frac{3}{5z}x^{-1-1}$$

Do the arithmetic.

$$\left(-\frac{3}{5z}\right)x^{-2}$$