Solve 2(x^9y^5)/4x^2

$$\frac { 2 ( x ^ { 9 } y ^ { 5 } ) } { 4 x ^ { 2 } }$$

Differentiate w.r.t. x

$$\frac{7y^{5}x^{6}}{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2y^{5}}{4}x^{9-2})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$\frac{7y^{5}}{2}x^{6}$$

Evaluate

$$\frac{y^{5}x^{7}}{2}$$

Solution Steps

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

$$\frac{y^{5}x^{7}}{2}$$