Solve frac{28x^{5}y^12z^10}{4x^3yz^5}

$$\frac { 28 x ^ { 5 } y ^ { 12 } z ^ { 10 } } { 4 x ^ { 3 } y z ^ { 5 } }$$

Differentiate w.r.t. x

$$14xz^{5}y^{11}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{28z^{10}y^{12}}{4yz^{5}}x^{5-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7z^{5}y^{11}x^{2})$$

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}.

$$2\times 7z^{5}y^{11}x^{2-1}$$

Do the arithmetic.

$$14z^{5}y^{11}x^{1}$$

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

$$14z^{5}y^{11}x$$

Evaluate

$$7x^{2}z^{5}y^{11}$$

Solution Steps

Cancel out 4yx^{3}z^{5} in both numerator and denominator.

$$7x^{2}z^{5}y^{11}$$