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Differentiate w.r.t. n
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64^{\frac{4}{3}}\left(n^{3}\right)^{\frac{4}{3}}
Expand \left(64n^{3}\right)^{\frac{4}{3}}.
64^{\frac{4}{3}}n^{4}
To raise a power to another power, multiply the exponents. Multiply 3 and \frac{4}{3} to get 4.
256n^{4}
Calculate 64 to the power of \frac{4}{3} and get 256.
\frac{4}{3}\times \left(64n^{3}\right)^{\frac{4}{3}-1}\frac{\mathrm{d}}{\mathrm{d}n}(64n^{3})
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).
\frac{4}{3}\sqrt[3]{64n^{3}}\times 3\times 64n^{3-1}
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}.
256n^{2}\sqrt[3]{64n^{3}}
Simplify.