Solve 18x^2e^216x^2e^2/6{x^2{e}^2}

$$\frac{ 18 { x }^{ 2 } { e }^{ 2 } 16 { x }^{ 2 } { e }^{ 2 } }{ 6 { x }^{ 2 } { e }^{ 2 } }$$

Evaluate

$$48\left(ex\right)^{2}$$

Solution Steps

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

$$\frac{18x^{4}e^{2}\times 16e^{2}}{6x^{2}e^{2}}$$

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

$$\frac{18x^{4}e^{4}\times 16}{6x^{2}e^{2}}$$

Cancel out 6e^{2}x^{2} in both numerator and denominator.

$$3\times 16e^{2}x^{2}$$

Multiply 3 and 16 to get 48.

$$48e^{2}x^{2}$$

Differentiate w.r.t. x

$$96e^{2}x$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{288e^{4}x^{2}}{6e^{2}}x^{2-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(48e^{2}x^{2}x^{0})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(48e^{2}x^{2})$$

The derivative of a constant term is 0.

$$0$$