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Evaluate
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Differentiate w.r.t. x
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\frac{z^{-4}x^{-3}}{x^{-5}z^{-3}}
Cancel out \frac{1}{y} in both numerator and denominator.
\frac{z^{-4}x^{2}}{z^{-3}}
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\frac{x^{2}}{z^{1}}
To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.
\frac{x^{2}}{z}
Calculate z to the power of 1 and get z.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{yz^{4}\times \frac{1}{yz^{3}}}x^{-3-\left(-5\right)})
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{z}x^{2})
Do the arithmetic.
2\times \frac{1}{z}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}.
\frac{2}{z}x^{1}
Do the arithmetic.
\frac{2}{z}x
For any term t, t^{1}=t.