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Differentiate w.r.t. k
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\left(4k+k\sqrt{3}\right)\left(4-\sqrt{3}\right)
Use the distributive property to multiply k by 4+\sqrt{3}.
16k-4\sqrt{3}k+4k\sqrt{3}-k\left(\sqrt{3}\right)^{2}
Apply the distributive property by multiplying each term of 4k+k\sqrt{3} by each term of 4-\sqrt{3}.
16k-k\left(\sqrt{3}\right)^{2}
Combine -4\sqrt{3}k and 4k\sqrt{3} to get 0.
16k-k\times 3
The square of \sqrt{3} is 3.
16k-3k
Multiply -1 and 3 to get -3.
13k
Combine 16k and -3k to get 13k.
\frac{\mathrm{d}}{\mathrm{d}k}(\left(4k+k\sqrt{3}\right)\left(4-\sqrt{3}\right))
Use the distributive property to multiply k by 4+\sqrt{3}.
\frac{\mathrm{d}}{\mathrm{d}k}(16k-4\sqrt{3}k+4k\sqrt{3}-k\left(\sqrt{3}\right)^{2})
Apply the distributive property by multiplying each term of 4k+k\sqrt{3} by each term of 4-\sqrt{3}.
\frac{\mathrm{d}}{\mathrm{d}k}(16k-k\left(\sqrt{3}\right)^{2})
Combine -4\sqrt{3}k and 4k\sqrt{3} to get 0.
\frac{\mathrm{d}}{\mathrm{d}k}(16k-k\times 3)
The square of \sqrt{3} is 3.
\frac{\mathrm{d}}{\mathrm{d}k}(16k-3k)
Multiply -1 and 3 to get -3.
\frac{\mathrm{d}}{\mathrm{d}k}(13k)
Combine 16k and -3k to get 13k.
13k^{1-1}
The derivative of ax^{n} is nax^{n-1}.
13k^{0}
Subtract 1 from 1.
13\times 1
For any term t except 0, t^{0}=1.
13
For any term t, t\times 1=t and 1t=t.