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Differentiate w.r.t. x
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\left(486x^{4}\right)^{1}\times \frac{1}{4x^{2}}
Use the rules of exponents to simplify the expression.
486^{1}\left(x^{4}\right)^{1}\times \frac{1}{4}\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.
486^{1}\times \frac{1}{4}\left(x^{4}\right)^{1}\times \frac{1}{x^{2}}
Use the Commutative Property of Multiplication.
486^{1}\times \frac{1}{4}x^{4}x^{2\left(-1\right)}
To raise a power to another power, multiply the exponents.
486^{1}\times \frac{1}{4}x^{4}x^{-2}
Multiply 2 times -1.
486^{1}\times \frac{1}{4}x^{4-2}
To multiply powers of the same base, add their exponents.
486^{1}\times \frac{1}{4}x^{2}
Add the exponents 4 and -2.
486\times \frac{1}{4}x^{2}
Raise 486 to the power 1.
\frac{243}{2}x^{2}
Multiply 486 times \frac{1}{4}.
\frac{486^{1}x^{4}}{4^{1}x^{2}}
Use the rules of exponents to simplify the expression.
\frac{486^{1}x^{4-2}}{4^{1}}
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\frac{486^{1}x^{2}}{4^{1}}
Subtract 2 from 4.
\frac{243}{2}x^{2}
Reduce the fraction \frac{486}{4} to lowest terms by extracting and canceling out 2.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{486}{4}x^{4-2})
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{243}{2}x^{2})
Do the arithmetic.
2\times \frac{243}{2}x^{2-1}
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}.
243x^{1}
Do the arithmetic.
243x
For any term t, t^{1}=t.