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Differentiate w.r.t. x
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\frac{x^{4}x^{3}}{x\times \frac{1}{2}xx\times \frac{1}{2}}\times \frac{x\times \frac{1}{2}xx\times \frac{1}{2}}{x^{2}xx^{3}}
To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.
\frac{x^{7}}{x\times \frac{1}{2}xx\times \frac{1}{2}}\times \frac{x\times \frac{1}{2}xx\times \frac{1}{2}}{x^{2}xx^{3}}
To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.
\frac{x^{7}}{x^{2}\times \frac{1}{2}x\times \frac{1}{2}}\times \frac{x\times \frac{1}{2}xx\times \frac{1}{2}}{x^{2}xx^{3}}
Multiply x and x to get x^{2}.
\frac{x^{7}}{x^{3}\times \frac{1}{2}\times \frac{1}{2}}\times \frac{x\times \frac{1}{2}xx\times \frac{1}{2}}{x^{2}xx^{3}}
To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.
\frac{x^{7}}{x^{3}\times \frac{1}{2}\times \frac{1}{2}}\times \frac{x^{2}\times \frac{1}{2}x\times \frac{1}{2}}{x^{2}xx^{3}}
Multiply x and x to get x^{2}.
\frac{x^{7}}{x^{3}\times \frac{1}{2}\times \frac{1}{2}}\times \frac{x^{3}\times \frac{1}{2}\times \frac{1}{2}}{x^{2}xx^{3}}
To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.
\frac{x^{7}}{x^{3}\times \frac{1}{2}\times \frac{1}{2}}\times \frac{x^{3}\times \frac{1}{2}\times \frac{1}{2}}{x^{3}x^{3}}
To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.
\frac{x^{7}}{x^{3}\times \frac{1}{2}\times \frac{1}{2}}\times \frac{x^{3}\times \frac{1}{2}\times \frac{1}{2}}{x^{6}}
To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.
\frac{x^{4}}{\frac{1}{2}\times \frac{1}{2}}\times \frac{x^{3}\times \frac{1}{2}\times \frac{1}{2}}{x^{6}}
Cancel out x^{3} in both numerator and denominator.
\frac{x^{4}}{\frac{1}{4}}\times \frac{x^{3}\times \frac{1}{2}\times \frac{1}{2}}{x^{6}}
Multiply \frac{1}{2} and \frac{1}{2} to get \frac{1}{4}.
x^{4}\times 4\times \frac{x^{3}\times \frac{1}{2}\times \frac{1}{2}}{x^{6}}
Divide x^{4} by \frac{1}{4} by multiplying x^{4} by the reciprocal of \frac{1}{4}.
x^{4}\times 4\times \frac{\frac{1}{2}\times \frac{1}{2}}{x^{3}}
Cancel out x^{3} in both numerator and denominator.
x^{4}\times 4\times \frac{\frac{1}{4}}{x^{3}}
Multiply \frac{1}{2} and \frac{1}{2} to get \frac{1}{4}.
x^{4}\times 4\times \frac{1}{4x^{3}}
Express \frac{\frac{1}{4}}{x^{3}} as a single fraction.
\frac{x^{4}}{4x^{3}}\times 4
Express x^{4}\times \frac{1}{4x^{3}} as a single fraction.
\frac{x}{4}\times 4
Cancel out x^{3} in both numerator and denominator.
x
Cancel out 4 and 4.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{4}x^{3}}{x\times \frac{1}{2}xx\times \frac{1}{2}}\times \frac{x\times \frac{1}{2}xx\times \frac{1}{2}}{x^{2}xx^{3}})
To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{7}}{x\times \frac{1}{2}xx\times \frac{1}{2}}\times \frac{x\times \frac{1}{2}xx\times \frac{1}{2}}{x^{2}xx^{3}})
To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{7}}{x^{2}\times \frac{1}{2}x\times \frac{1}{2}}\times \frac{x\times \frac{1}{2}xx\times \frac{1}{2}}{x^{2}xx^{3}})
Multiply x and x to get x^{2}.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{7}}{x^{3}\times \frac{1}{2}\times \frac{1}{2}}\times \frac{x\times \frac{1}{2}xx\times \frac{1}{2}}{x^{2}xx^{3}})
To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{7}}{x^{3}\times \frac{1}{2}\times \frac{1}{2}}\times \frac{x^{2}\times \frac{1}{2}x\times \frac{1}{2}}{x^{2}xx^{3}})
Multiply x and x to get x^{2}.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{7}}{x^{3}\times \frac{1}{2}\times \frac{1}{2}}\times \frac{x^{3}\times \frac{1}{2}\times \frac{1}{2}}{x^{2}xx^{3}})
To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{7}}{x^{3}\times \frac{1}{2}\times \frac{1}{2}}\times \frac{x^{3}\times \frac{1}{2}\times \frac{1}{2}}{x^{3}x^{3}})
To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{7}}{x^{3}\times \frac{1}{2}\times \frac{1}{2}}\times \frac{x^{3}\times \frac{1}{2}\times \frac{1}{2}}{x^{6}})
To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{4}}{\frac{1}{2}\times \frac{1}{2}}\times \frac{x^{3}\times \frac{1}{2}\times \frac{1}{2}}{x^{6}})
Cancel out x^{3} in both numerator and denominator.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{4}}{\frac{1}{4}}\times \frac{x^{3}\times \frac{1}{2}\times \frac{1}{2}}{x^{6}})
Multiply \frac{1}{2} and \frac{1}{2} to get \frac{1}{4}.
\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}\times 4\times \frac{x^{3}\times \frac{1}{2}\times \frac{1}{2}}{x^{6}})
Divide x^{4} by \frac{1}{4} by multiplying x^{4} by the reciprocal of \frac{1}{4}.
\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}\times 4\times \frac{\frac{1}{2}\times \frac{1}{2}}{x^{3}})
Cancel out x^{3} in both numerator and denominator.
\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}\times 4\times \frac{\frac{1}{4}}{x^{3}})
Multiply \frac{1}{2} and \frac{1}{2} to get \frac{1}{4}.
\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}\times 4\times \frac{1}{4x^{3}})
Express \frac{\frac{1}{4}}{x^{3}} as a single fraction.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{4}}{4x^{3}}\times 4)
Express x^{4}\times \frac{1}{4x^{3}} as a single fraction.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{4}\times 4)
Cancel out x^{3} in both numerator and denominator.
\frac{\mathrm{d}}{\mathrm{d}x}(x)
Cancel out 4 and 4.
x^{1-1}
The derivative of ax^{n} is nax^{n-1}.
x^{0}
Subtract 1 from 1.
1
For any term t except 0, t^{0}=1.