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Evaluate
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Differentiate w.r.t. y
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\left(y^{4}\right)^{2}
Use the rules of exponents to simplify the expression.
y^{4\times 2}
To raise a power to another power, multiply the exponents.
y^{8}
Multiply 4 times 2.
2\left(y^{4}\right)^{2-1}\frac{\mathrm{d}}{\mathrm{d}y}(y^{4})
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).
2\left(y^{4}\right)^{1}\times 4y^{4-1}
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}.
8y^{3}\left(y^{4}\right)^{1}
Simplify.
8y^{3}y^{4}
For any term t, t^{1}=t.