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Differentiate w.r.t. p
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\frac{1}{3p^{-5}}
Use the rules of exponents to simplify the expression.
\frac{1}{3}\times \frac{1}{p^{-5}}
To raise the product of two or more numbers to a power, raise each number to the power and take their product.
\frac{1}{3}p^{-5\left(-1\right)}
To raise a power to another power, multiply the exponents.
\frac{1}{3}p^{5}
Multiply -5 times -1.
-\left(3p^{-5}\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}p}(3p^{-5})
If F is the composition of two differentiable functions f\left(u\right) and u=g\left(x\right), that is, if F\left(x\right)=f\left(g\left(x\right)\right), then the derivative of F is the derivative of f with respect to u times the derivative of g with respect to x, that is, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).
-\left(3p^{-5}\right)^{-2}\left(-5\right)\times 3p^{-5-1}
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}.
15p^{-6}\times \left(3p^{-5}\right)^{-2}
Simplify.