Solve -2d/dt(7*10e^-4e^-frac{1{7}})

$$- \frac { 2 d } { d t } ( 7 \times 10 e ^ { - 4 } e ^ { - \frac { 1 } { 7 } } )$$

Evaluate

$$-\frac{140}{e^{\frac{29}{7}}t}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -4 and -\frac{1}{7} to get -\frac{29}{7}.

$$\left(-\frac{2d}{dt}\right)\times 7\times 10e^{-\frac{29}{7}}$$

Cancel out d in both numerator and denominator.

$$\left(-\frac{2}{t}\right)\times 7\times 10e^{-\frac{29}{7}}$$

Multiply 7 and 10 to get 70.

$$\left(-\frac{2}{t}\right)\times 70e^{-\frac{29}{7}}$$

Express \left(-\frac{2}{t}\right)\times 70 as a single fraction.

$$\frac{-2\times 70}{t}e^{-\frac{29}{7}}$$

Multiply -2 and 70 to get -140.

$$\frac{-140}{t}e^{-\frac{29}{7}}$$

Differentiate w.r.t. t

$$\frac{140}{e^{\frac{29}{7}}t^{2}}$$