Solve 15x^4y^3/10x^7y^2z

$$\frac { 15 x ^ { 4 } y ^ { 3 } } { 10 x ^ { 7 } y ^ { 2 } z }$$

Differentiate w.r.t. x

$$-\frac{9y}{2zx^{4}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{15y^{3}}{10zy^{2}}x^{4-7})$$

Do the arithmetic.

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

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}.

$$-3\times \frac{3y}{2z}x^{-3-1}$$

Do the arithmetic.

$$\left(-\frac{9y}{2z}\right)x^{-4}$$

Evaluate

$$\frac{3y}{2zx^{3}}$$

Solution Steps

Cancel out 5y^{2}x^{4} in both numerator and denominator.

$$\frac{3y}{2zx^{3}}$$