Solve t^36/t^3t^4

$$\frac { t ^ { 36 } } { t ^ { 3 } t ^ { 4 } }$$

Evaluate

$$t^{29}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{t^{36}}{t^{7}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 7 from 36 to get 29.

$$t^{29}$$

Differentiate w.r.t. t

$$29t^{28}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{t^{36}}{t^{7}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 7 from 36 to get 29.

$$\frac{\mathrm{d}}{\mathrm{d}t}(t^{29})$$

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

$$29t^{29-1}$$

Subtract 1 from 29.

$$29t^{28}$$