Solve 85x^6y^3z/-9x^3y^2x

$$\frac{ 85 { x }^{ 6 } { y }^{ 3 } z }{ -9 { x }^{ 3 } { y }^{ 2 } x }$$

Evaluate

$$-\frac{85yzx^{2}}{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{85x^{6}y^{3}z}{-9x^{4}y^{2}}$$

Cancel out y^{2}x^{4} in both numerator and denominator.

$$\frac{85yzx^{2}}{-9}$$

Differentiate w.r.t. x

$$-\frac{170xyz}{9}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{85zy^{3}}{-9xy^{2}}x^{6-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{85yz}{9x}\right)x^{3})$$

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}.

$$3\left(-\frac{85yz}{9x}\right)x^{3-1}$$

Do the arithmetic.

$$\left(-\frac{85yz}{3x}\right)x^{2}$$