Solve -t^10divt^3divt^2

$$- t ^ { 10 } \div t ^ { 3 } \div t ^ { 2 }$$

Evaluate

$$-t^{5}$$

Solution Steps

Express \frac{\frac{-t^{10}}{t^{3}}}{t^{2}} as a single fraction.

$$\frac{-t^{10}}{t^{3}t^{2}}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{-t^{10}}{t^{5}}$$

Cancel out t^{5} in both numerator and denominator.

$$-t^{5}$$

Differentiate w.r.t. t

$$-5t^{4}$$

Steps Using Definition of a Derivative

Express \frac{\frac{-t^{10}}{t^{3}}}{t^{2}} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{-t^{10}}{t^{3}t^{2}})$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{-t^{10}}{t^{5}})$$

Cancel out t^{5} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}t}(-t^{5})$$

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

$$5\left(-1\right)t^{5-1}$$

Multiply 5 times -1.

$$-5t^{5-1}$$

Subtract 1 from 5.

$$-5t^{4}$$