Solve 10*x^9/2621+1*4(45)*x^8/65536*2^8(120)*x^2/16384*16

$$10 \times \frac { x ^ { 9 } } { 2621 + 1 } \times 4 ( 45 ) \times \frac { x ^ { 8 } } { 65536 } \times 2 ^ { 8 } ( 120 ) \times \frac { x ^ { 2 } } { 16384 } \times 16$$

Evaluate

$$\frac{1125x^{19}}{3579904}$$

Solution Steps

Add 2621 and 1 to get 2622.

$$10\times \frac{x^{9}}{2622}\times 4\times 45\times \frac{x^{8}}{65536}\times 2^{8}\times 120\times \frac{x^{2}}{16384}\times 16$$

Multiply 10 and 4 to get 40.

$$40\times \frac{x^{9}}{2622}\times 45\times \frac{x^{8}}{65536}\times 2^{8}\times 120\times \frac{x^{2}}{16384}\times 16$$

Multiply 40 and 45 to get 1800.

$$1800\times \frac{x^{9}}{2622}\times \frac{x^{8}}{65536}\times 2^{8}\times 120\times \frac{x^{2}}{16384}\times 16$$

Calculate 2 to the power of 8 and get 256.

$$1800\times \frac{x^{9}}{2622}\times \frac{x^{8}}{65536}\times 256\times 120\times \frac{x^{2}}{16384}\times 16$$

Multiply 1800 and 256 to get 460800.

$$460800\times \frac{x^{9}}{2622}\times \frac{x^{8}}{65536}\times 120\times \frac{x^{2}}{16384}\times 16$$

Multiply 460800 and 120 to get 55296000.

$$55296000\times \frac{x^{9}}{2622}\times \frac{x^{8}}{65536}\times \frac{x^{2}}{16384}\times 16$$

Multiply 55296000 and 16 to get 884736000.

$$884736000\times \frac{x^{9}}{2622}\times \frac{x^{8}}{65536}\times \frac{x^{2}}{16384}$$

Express 884736000\times \frac{x^{9}}{2622} as a single fraction.

$$\frac{884736000x^{9}}{2622}\times \frac{x^{8}}{65536}\times \frac{x^{2}}{16384}$$

Multiply \frac{884736000x^{9}}{2622} times \frac{x^{8}}{65536} by multiplying numerator times numerator and denominator times denominator.

$$\frac{884736000x^{9}x^{8}}{2622\times 65536}\times \frac{x^{2}}{16384}$$

Cancel out 6\times 65536 in both numerator and denominator.

$$\frac{2250x^{8}x^{9}}{437}\times \frac{x^{2}}{16384}$$

Multiply \frac{2250x^{8}x^{9}}{437} times \frac{x^{2}}{16384} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2250x^{8}x^{9}x^{2}}{437\times 16384}$$

Cancel out 2 in both numerator and denominator.

$$\frac{1125x^{2}x^{8}x^{9}}{437\times 8192}$$

To multiply powers of the same base, add their exponents. Add 2 and 8 to get 10.

$$\frac{1125x^{10}x^{9}}{437\times 8192}$$

To multiply powers of the same base, add their exponents. Add 10 and 9 to get 19.

$$\frac{1125x^{19}}{437\times 8192}$$

Multiply 437 and 8192 to get 3579904.

$$\frac{1125x^{19}}{3579904}$$

Differentiate w.r.t. x

$$\frac{1125x^{18}}{188416}$$