Solve 2pi2.25lambda/1.005*10^4*0.9

$$\frac { 2 \pi 2.25 \lambda } { 1.005 \times 10 ^ { 4 } } \times 0.9$$

Evaluate

$$\frac{27\pi \lambda }{67000}$$

Solution Steps

Multiply 2 and 2.25 to get 4.5.

$$\frac{4.5\pi \lambda }{1.005\times 10^{4}}\times 0.9$$

Calculate 10 to the power of 4 and get 10000.

$$\frac{4.5\pi \lambda }{1.005\times 10000}\times 0.9$$

Multiply 1.005 and 10000 to get 10050.

$$\frac{4.5\pi \lambda }{10050}\times 0.9$$

Divide 4.5\pi \lambda by 10050 to get \frac{3}{6700}\pi \lambda .

$$\frac{3}{6700}\pi \lambda \times 0.9$$

Multiply \frac{3}{6700} and 0.9 to get \frac{27}{67000}.

$$\frac{27}{67000}\pi \lambda$$

Differentiate w.r.t. λ

$$\frac{27 \pi}{67000} = 0.0012660149499540956$$