Solve -3x^4y^3/-4x^-4y^0*{x^2{y}^3}

$$\frac{ -3 { x }^{ 4 } { y }^{ 3 } }{ -4 { x }^{ -4 } { y }^{ 0 } \times { x }^{ 2 } { y }^{ 3 } }$$

Evaluate

$$\frac{3x^{6}}{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -4 and 2 to get -2.

$$\frac{-3x^{4}y^{3}}{-4x^{-2}y^{0}y^{3}}$$

To multiply powers of the same base, add their exponents. Add 0 and 3 to get 3.

$$\frac{-3x^{4}y^{3}}{-4x^{-2}y^{3}}$$

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

$$\frac{-3x^{4}}{-4x^{-2}}$$

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

$$\frac{-3x^{6}}{-4}$$

Differentiate w.r.t. x

$$\frac{9x^{5}}{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{3y^{3}}{-4y^{0}x^{2}y^{3}}\right)x^{4-\left(-4\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{4x^{2}}x^{8})$$

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}.

$$8\times \frac{3}{4x^{2}}x^{8-1}$$

Do the arithmetic.

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