Solve 6xy^5z^3/2y^-2x^-4

$$\frac{ 6x { y }^{ 5 } { z }^{ 3 } }{ 2 { y }^{ -2 } { x }^{ -4 } }$$

Evaluate

$$3z^{3}x^{5}y^{7}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{3xz^{3}y^{5}}{x^{-4}y^{-2}}$$

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

$$3z^{3}x^{5}y^{7}$$

Differentiate w.r.t. x

$$15z^{3}x^{4}y^{7}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6z^{3}y^{5}y^{2}}{2}x^{1-\left(-4\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3z^{3}y^{7}x^{5})$$

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}.

$$5\times 3z^{3}y^{7}x^{5-1}$$

Do the arithmetic.

$$15z^{3}y^{7}x^{4}$$