Solve 7t^5(-6t^5)

$$7 t ^ { 5 } ( - 6 t ^ { 5 } )$$

Evaluate

$$-42t^{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 5 to get 10.

$$7t^{10}\left(-6\right)$$

Multiply 7 and -6 to get -42.

$$-42t^{10}$$

Differentiate w.r.t. t

$$-420t^{9}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 5 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}t}(7t^{10}\left(-6\right))$$

Multiply 7 and -6 to get -42.

$$\frac{\mathrm{d}}{\mathrm{d}t}(-42t^{10})$$

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

$$10\left(-42\right)t^{10-1}$$

Multiply 10 times -42.

$$-420t^{10-1}$$

Subtract 1 from 10.

$$-420t^{9}$$