Solve frac{(-2,4)^{2}*10x^3y^11}{8x^10y^4}

$$\frac { ( - 2,4 ) ^ { 2 } \cdot 10 x ^ { 3 } y ^ { 11 } } { 8 x ^ { 10 } y ^ { 4 } }$$

Evaluate

$$\frac{36\times \left(\frac{y}{x}\right)^{7}}{5}$$

Solution Steps

Cancel out 2x^{3}y^{4} in both numerator and denominator.

$$\frac{5\left(-2,4\right)^{2}y^{7}}{4x^{7}}$$

Calculate -2,4 to the power of 2 and get 5,76.

$$\frac{5\times 5,76y^{7}}{4x^{7}}$$

Multiply 5 and 5,76 to get 28,8.

$$\frac{28,8y^{7}}{4x^{7}}$$

Differentiate w.r.t. x

$$-\frac{252y^{7}}{5x^{8}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{57,6y^{11}}{8y^{4}}x^{3-10})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{36y^{7}}{5}x^{-7})$$

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}.

$$-7\times \frac{36y^{7}}{5}x^{-7-1}$$

Do the arithmetic.

$$\left(-\frac{252y^{7}}{5}\right)x^{-8}$$