Evaluate
\frac{y^{9}}{3}
Differentiate w.r.t. y
3y^{8}
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\frac{x^{2}y^{5}}{3}\times \frac{y^{4}}{x^{2}}
Cancel out x in both numerator and denominator.
\frac{x^{2}y^{5}y^{4}}{3x^{2}}
Multiply \frac{x^{2}y^{5}}{3} times \frac{y^{4}}{x^{2}} by multiplying numerator times numerator and denominator times denominator.
\frac{y^{4}y^{5}}{3}
Cancel out x^{2} in both numerator and denominator.
\frac{y^{9}}{3}
To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.
\frac{\mathrm{d}}{\mathrm{d}y}(\frac{x^{2}y^{5}}{3}\times \frac{y^{4}}{x^{2}})
Cancel out x in both numerator and denominator.
\frac{\mathrm{d}}{\mathrm{d}y}(\frac{x^{2}y^{5}y^{4}}{3x^{2}})
Multiply \frac{x^{2}y^{5}}{3} times \frac{y^{4}}{x^{2}} by multiplying numerator times numerator and denominator times denominator.
\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y^{4}y^{5}}{3})
Cancel out x^{2} in both numerator and denominator.
\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y^{9}}{3})
To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.
9\times \frac{1}{3}y^{9-1}
The derivative of ax^{n} is nax^{n-1}.
3y^{9-1}
Multiply 9 times \frac{1}{3}.
3y^{8}
Subtract 1 from 9.