Solve 2*10^-7(lne^frac{1{4}}+x)

$$2 \times 10 ^ { - 7 } ( \ln e ^ { \frac { 1 } { 4 } } + x )$$

Evaluate

$$\frac{x}{5000000}+\frac{1}{20000000}$$

Solution Steps

Calculate 10 to the power of -7 and get \frac{1}{10000000}.

$$2\times \frac{1}{10000000}\left(\log_{e}\left(e^{\frac{1}{4}}\right)+x\right)$$

Multiply 2 and \frac{1}{10000000} to get \frac{1}{5000000}.

$$\frac{1}{5000000}\left(\log_{e}\left(e^{\frac{1}{4}}\right)+x\right)$$

Use the distributive property to multiply \frac{1}{5000000} by \log_{e}\left(e^{\frac{1}{4}}\right)+x.

$$\frac{1}{5000000}\log_{e}\left(e^{\frac{1}{4}}\right)+\frac{1}{5000000}x$$

Differentiate w.r.t. x

$$\frac{1}{5000000} = 2 \times 10^{-7}$$