Solve frac{10^{5}x6^5x24}{48^2x15^4x4^3}

$$\frac { 10 ^ { 5 } x 6 ^ { 5 } x 24 } { 48 ^ { 2 } x 15 ^ { 4 } x 4 ^ { 3 } }$$

Evaluate

$$\frac{5x_{24}}{48x}$$

Solution Steps

Multiply x and x to get x^{2}.

$$\frac{10^{5}x\times 6^{5}x_{24}}{48^{2}x^{2}\times 15^{4}\times 4^{3}}$$

Cancel out x in both numerator and denominator.

$$\frac{6^{5}\times 10^{5}x_{24}}{4^{3}\times 15^{4}\times 48^{2}x}$$

Calculate 6 to the power of 5 and get 7776.

$$\frac{7776\times 10^{5}x_{24}}{4^{3}\times 15^{4}\times 48^{2}x}$$

Calculate 10 to the power of 5 and get 100000.

$$\frac{7776\times 100000x_{24}}{4^{3}\times 15^{4}\times 48^{2}x}$$

Multiply 7776 and 100000 to get 777600000.

$$\frac{777600000x_{24}}{4^{3}\times 15^{4}\times 48^{2}x}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{777600000x_{24}}{64\times 15^{4}\times 48^{2}x}$$

Calculate 15 to the power of 4 and get 50625.

$$\frac{777600000x_{24}}{64\times 50625\times 48^{2}x}$$

Multiply 64 and 50625 to get 3240000.

$$\frac{777600000x_{24}}{3240000\times 48^{2}x}$$

Calculate 48 to the power of 2 and get 2304.

$$\frac{777600000x_{24}}{3240000\times 2304x}$$

Multiply 3240000 and 2304 to get 7464960000.

$$\frac{777600000x_{24}}{7464960000x}$$

Cancel out 155520000 in both numerator and denominator.

$$\frac{5x_{24}}{48x}$$

Differentiate w.r.t. x

$$-\frac{5x_{24}}{48x^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{777600000x_{24}}{7464960000x}x^{1-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x_{24}}{48x}x^{0})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x_{24}}{48x})$$

The derivative of a constant term is 0.

$$0$$