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Differentiate w.r.t. x
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x^{27}\frac{\mathrm{d}}{\mathrm{d}x}(x^{13})+x^{13}\frac{\mathrm{d}}{\mathrm{d}x}(x^{27})
For any two differentiable functions, the derivative of the product of two functions is the first function times the derivative of the second plus the second function times the derivative of the first.
x^{27}\times 13x^{13-1}+x^{13}\times 27x^{27-1}
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}.
x^{27}\times 13x^{12}+x^{13}\times 27x^{26}
Simplify.
13x^{27+12}+27x^{13+26}
To multiply powers of the same base, add their exponents.
13x^{39}+27x^{39}
Simplify.
x^{40}
To multiply powers of the same base, add their exponents. Add 27 and 13 to get 40.