Solve 81x^2*9x^2y^2/3^6{x^2{y}^2}

$$\frac{ 81 { x }^{ 2 } \times 9 { x }^{ 2 } { y }^{ 2 } }{ { 3 }^{ 6 } { x }^{ 2 } { y }^{ 2 } }$$

Evaluate

$$x^{2}$$

Solution Steps

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

$$\frac{81x^{4}\times 9y^{2}}{3^{6}x^{2}y^{2}}$$

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

$$\frac{9\times 81x^{2}}{3^{6}}$$

Multiply 9 and 81 to get 729.

$$\frac{729x^{2}}{3^{6}}$$

Calculate 3 to the power of 6 and get 729.

$$\frac{729x^{2}}{729}$$

Cancel out 729 and 729.

$$x^{2}$$

Differentiate w.r.t. x

$$2x$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{729x^{2}y^{2}}{729y^{2}}x^{2-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}x^{0})$$

For any number a except 0, a^{0}=1.

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

The derivative of a constant term is 0.

$$0$$