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Differentiate w.r.t. u
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\left(16u^{1}\right)^{1}\times \frac{1}{4u^{5}}
Use the rules of exponents to simplify the expression.
16^{1}\left(u^{1}\right)^{1}\times \frac{1}{4}\times \frac{1}{u^{5}}
To raise the product of two or more numbers to a power, raise each number to the power and take their product.
16^{1}\times \frac{1}{4}\left(u^{1}\right)^{1}\times \frac{1}{u^{5}}
Use the Commutative Property of Multiplication.
16^{1}\times \frac{1}{4}u^{1}u^{5\left(-1\right)}
To raise a power to another power, multiply the exponents.
16^{1}\times \frac{1}{4}u^{1}u^{-5}
Multiply 5 times -1.
16^{1}\times \frac{1}{4}u^{1-5}
To multiply powers of the same base, add their exponents.
16^{1}\times \frac{1}{4}u^{-4}
Add the exponents 1 and -5.
16\times \frac{1}{4}u^{-4}
Raise 16 to the power 1.
4u^{-4}
Multiply 16 times \frac{1}{4}.
\frac{16^{1}u^{1}}{4^{1}u^{5}}
Use the rules of exponents to simplify the expression.
\frac{16^{1}u^{1-5}}{4^{1}}
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\frac{16^{1}u^{-4}}{4^{1}}
Subtract 5 from 1.
4u^{-4}
Divide 16 by 4.
\frac{\mathrm{d}}{\mathrm{d}u}(\frac{16}{4}u^{1-5})
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\frac{\mathrm{d}}{\mathrm{d}u}(4u^{-4})
Do the arithmetic.
-4\times 4u^{-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}.
-16u^{-5}
Do the arithmetic.