Solve 8x^34(3x^2)4x^2/x/7x^2sqrt{7{pi^2}38x/9}

$$\frac{ 8 { x }^{ 3 } 4(3 { x }^{ 2 } ) \frac { 4 { x }^{ 2 } } { x } }{ 7 { x }^{ 2 } \sqrt{ 7 { \pi }^{ 2 } } \frac { 38x } { 9 } }$$

Differentiate w.r.t. x

$$\frac{5184\sqrt{7}x^{2}}{931\pi }$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{96\times \frac{4x^{2}}{x}x^{2}}{7\sqrt{7\pi ^{2}}\times \frac{38x}{9}}x^{3-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1728\sqrt{7}x^{2}}{931\pi }x^{1})$$

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}.

$$\frac{1728\sqrt{7}x^{2}}{931\pi }x^{1-1}$$

Do the arithmetic.

$$\frac{1728\sqrt{7}x^{2}}{931\pi }x^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{1728\sqrt{7}x^{2}}{931\pi }\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{1728\sqrt{7}x^{2}}{931\pi }$$

Evaluate

$$\frac{1728\sqrt{7}x^{3}}{931\pi }$$