Solve 009t^1-t^6

$$009 t ^ { 1 } - t ^ { 6 }$$

Evaluate

$$-t^{6}$$

Solution Steps

Multiply 0 and 0 to get 0.

$$0\times 9t^{1}-t^{6}$$

Multiply 0 and 9 to get 0.

$$0t^{1}-t^{6}$$

Calculate t to the power of 1 and get t.

$$0t-t^{6}$$

Anything times zero gives zero.

$$0-t^{6}$$

Anything plus zero gives itself.

$$-t^{6}$$

Differentiate w.r.t. t

$$-6t^{5}$$

Steps Using Definition of a Derivative

Multiply 0 and 0 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}t}(0\times 9t^{1}-t^{6})$$

Multiply 0 and 9 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}t}(0t^{1}-t^{6})$$

Calculate t to the power of 1 and get t.

$$\frac{\mathrm{d}}{\mathrm{d}t}(0t-t^{6})$$

Anything times zero gives zero.

$$\frac{\mathrm{d}}{\mathrm{d}t}(0-t^{6})$$

Anything plus zero gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}t}(-t^{6})$$

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

$$6\left(-1\right)t^{6-1}$$

Multiply 6 times -1.

$$-6t^{6-1}$$

Subtract 1 from 6.

$$-6t^{5}$$