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Evaluate
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Differentiate w.r.t. t
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\frac{t^{5}}{t^{9}}
Use the rules of exponents to simplify the expression.
t^{5-9}
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
t^{-4}
Subtract 9 from 5.
\frac{\mathrm{d}}{\mathrm{d}t}(\frac{1}{1}t^{5-9})
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\frac{\mathrm{d}}{\mathrm{d}t}(t^{-4})
Do the arithmetic.
-4t^{-4-1}
The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.
-4t^{-5}
Do the arithmetic.