Solve 4x^3y^3z^6/xyz^5

$$\frac { 4 x ^ { 3 } y ^ { 3 } z ^ { 6 } } { x y z ^ { 5 } }$$

Differentiate w.r.t. x

$$8xzy^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4y^{3}z^{6}}{yz^{5}}x^{3-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4zy^{2}x^{2})$$

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}.

$$2\times 4zy^{2}x^{2-1}$$

Do the arithmetic.

$$8zy^{2}x^{1}$$

For any term t, t^{1}=t.

$$8zy^{2}x$$

Evaluate

$$4z\left(xy\right)^{2}$$

Solution Steps

Cancel out xyz^{5} in both numerator and denominator.

$$4zx^{2}y^{2}$$