What is the d/(dz)((2z^6+2)/(1z^2+5)) ?

The d/(dz)((2z^6+2)/(1z^2+5)) is (8z^7+60z^5-4z)/((z^2+5)^2)

What is the first d/(dz)((2z^6+2)/(1z^2+5)) ?

The first d/(dz)((2z^6+2)/(1z^2+5)) is (8z^7+60z^5-4z)/((z^2+5)^2)

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\frac{d}{d z} (\frac{2 z ^{6} + 2}{1 z ^{2} + 5})

\frac{8 z ^{7} + 60 z ^{5} - 4 z}{( z ^{2} + 5 ) ^{2}}

Solution steps

\frac{d}{d z} (\frac{2 z ^{6} + 2}{1 \cdot z ^{2} + 5})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d z} ( 2 z ^{6} + 2 ) ( 1 \cdot z ^{2} + 5 ) - \frac{d}{d z} ( 1 \cdot z ^{2} + 5 ) ( 2 z ^{6} + 2 )}{( 1 \cdot z ^{2} + 5 ) ^{2}}

\frac{d}{d z} (2 z^{6} + 2) = 12 z^{5}

\frac{d}{d z} (1 \cdot z^{2} + 5) = 2 z

= \frac{12 z ^{5} ( 1 \cdot z ^{2} + 5 ) - 2 z ( 2 z ^{6} + 2 )}{( 1 \cdot z ^{2} + 5 ) ^{2}}

Simplify

\frac{12 z ^{5} ( 1 \cdot z ^{2} + 5 ) - 2 z ( 2 z ^{6} + 2 )}{( 1 \cdot z ^{2} + 5 ) ^{2}} : \frac{8 z ^{7} + 60 z ^{5} - 4 z}{( z ^{2} + 5 ) ^{2}}

= \frac{8 z ^{7} + 60 z ^{5} - 4 z}{( z ^{2} + 5 ) ^{2}}

n = 1 \sum \infty (\frac{e}{n})^{2 n}

\int cos^{4} (1) d x

\int 10 x ln (x + 5) d x

\int \frac{x}{8} d x

y^{^{'}} = y^{2}, y (0) = 1

What is the d/(dz)((2z^6+2)/(1z^2+5)) ?
The d/(dz)((2z^6+2)/(1z^2+5)) is (8z^7+60z^5-4z)/((z^2+5)^2)
What is the first d/(dz)((2z^6+2)/(1z^2+5)) ?
The first d/(dz)((2z^6+2)/(1z^2+5)) is (8z^7+60z^5-4z)/((z^2+5)^2)