Solve {2}^log_{2({7θ})}

$${ 2 }^{ \log_{ 2 }({ 7 \theta }) }$$

Differentiate w.r.t. θ

$$\frac{2^{\frac{\ln(\theta )+\ln(7)}{\ln(2)}}}{\theta }$$

Steps Using Definition of a Derivative

Apply rule a^{\log_{a}\left(b\right)}=b, where a=2 and b=7\theta .

$$\frac{\mathrm{d}}{\mathrm{d}\theta }(7\theta )$$

The derivative of ax^{n} is nax^{n-1}.

$$7\theta ^{1-1}$$

Subtract 1 from 1.

$$7\theta ^{0}$$

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

$$7\times 1$$

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

$$7$$

Evaluate

$$2^{\frac{\ln(\theta )+\ln(7)}{\ln(2)}}$$

Solution Steps

Apply rule a^{\log_{a}\left(b\right)}=b, where a=2 and b=7\theta .

$$7\theta$$