Solve 1.254110^9sin(1/1.254*10^9)

$$1.2541 { 10 }^{ 9 } \sin ( \frac{ 1 }{ 1.254 \times { 10 }^{ 9 } } )$$

Evaluate

$$\frac{43636710823885341753E}{25000000000}-11$$

Solution Steps

Evaluate trigonometric functions in the problem

$$1.2541 {(10)} ^ {9} 1.3918096108407732E-11$$

Calculate 10 to the power of 9 and get 1000000000.

$$1.2541\times 1000000000\times 1.3918096108407732E-11$$

Multiply 1.2541 and 1000000000 to get 1254100000.

$$1254100000\times 1.3918096108407732E-11$$

Multiply 1254100000 and 1.3918096108407732 to get 1745468432.95541367012.

$$1745468432.95541367012E-11$$

Differentiate w.r.t. E

$$1745468432.95541367012$$

Steps Using Derivative Rule for Sum

Evaluate trigonometric functions in the problem

$$1.2541 {(10)} ^ {9} 1.3918096108407732E-11$$

Calculate 10 to the power of 9 and get 1000000000.

$$\frac{\mathrm{d}}{\mathrm{d}E}(1.2541\times 1000000000\times 1.3918096108407732E-11)$$

Multiply 1.2541 and 1000000000 to get 1254100000.

$$\frac{\mathrm{d}}{\mathrm{d}E}(1254100000\times 1.3918096108407732E-11)$$

Multiply 1254100000 and 1.3918096108407732 to get 1745468432.95541367012.

$$\frac{\mathrm{d}}{\mathrm{d}E}(1745468432.95541367012E-11)$$

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}.

$$1745468432.95541367012E^{1-1}$$

Subtract 1 from 1.

$$1745468432.95541367012E^{0}$$

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

$$1745468432.95541367012\times 1$$

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

$$1745468432.95541367012$$