Solve 15/4x^3y^7z/frac{9{2}x^2y^7}

$$\frac { \frac { 15 } { 4 } x ^ { 3 } y ^ { 7 } z } { \frac { 9 } { 2 } x ^ { 2 } y ^ { 7 } }$$

Evaluate

$$\frac{5xz}{6}$$

Solution Steps

Cancel out x^{2}y^{7} in both numerator and denominator.

$$\frac{\frac{15}{4}xz}{\frac{9}{2}}$$

Divide \frac{15}{4}xz by \frac{9}{2} by multiplying \frac{15}{4}xz by the reciprocal of \frac{9}{2}.

$$\frac{\frac{15}{4}xz\times 2}{9}$$

Multiply \frac{15}{4} and 2 to get \frac{15}{2}.

$$\frac{\frac{15}{2}xz}{9}$$

Divide \frac{15}{2}xz by 9 to get \frac{5}{6}xz.

$$\frac{5}{6}xz$$

Differentiate w.r.t. x

$$\frac{5z}{6}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{15zy^{7}}{4\times \frac{9y^{7}}{2}}x^{3-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5z}{6}x^{1})$$

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}.

$$\frac{5z}{6}x^{1-1}$$

Do the arithmetic.

$$\frac{5z}{6}x^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{5z}{6}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{5z}{6}$$