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Differentiate w.r.t. x
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\left(20x^{5}\right)^{1}\times \frac{1}{10x^{2}}
Use the rules of exponents to simplify the expression.
20^{1}\left(x^{5}\right)^{1}\times \frac{1}{10}\times \frac{1}{x^{2}}
To raise the product of two or more numbers to a power, raise each number to the power and take their product.
20^{1}\times \frac{1}{10}\left(x^{5}\right)^{1}\times \frac{1}{x^{2}}
Use the Commutative Property of Multiplication.
20^{1}\times \frac{1}{10}x^{5}x^{2\left(-1\right)}
To raise a power to another power, multiply the exponents.
20^{1}\times \frac{1}{10}x^{5}x^{-2}
Multiply 2 times -1.
20^{1}\times \frac{1}{10}x^{5-2}
To multiply powers of the same base, add their exponents.
20^{1}\times \frac{1}{10}x^{3}
Add the exponents 5 and -2.
20\times \frac{1}{10}x^{3}
Raise 20 to the power 1.
2x^{3}
Multiply 20 times \frac{1}{10}.
\frac{20^{1}x^{5}}{10^{1}x^{2}}
Use the rules of exponents to simplify the expression.
\frac{20^{1}x^{5-2}}{10^{1}}
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\frac{20^{1}x^{3}}{10^{1}}
Subtract 2 from 5.
2x^{3}
Divide 20 by 10.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{20}{10}x^{5-2})
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3})
Do the arithmetic.
3\times 2x^{3-1}
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}.
6x^{2}
Do the arithmetic.