What is the derivative of ((5t-3)^7)/(8t^2+7) ?

The derivative of ((5t-3)^7)/(8t^2+7) is (35(5t-3)^6(8t^2+7)-16t(5t-3)^7)/((8t^2+7)^2)

What is the first derivative of ((5t-3)^7)/(8t^2+7) ?

The first derivative of ((5t-3)^7)/(8t^2+7) is (35(5t-3)^6(8t^2+7)-16t(5t-3)^7)/((8t^2+7)^2)

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derivative of

\frac{( 5 t - 3 ) ^{7}}{8 t ^{2} + 7}

\frac{35 ( 5 t - 3 ) ^{6} ( 8 t ^{2} + 7 ) - 16 t ( 5 t - 3 ) ^{7}}{( 8 t ^{2} + 7 ) ^{2}}

Solution steps

\frac{d}{d t} (\frac{( 5 t - 3 ) ^{7}}{8 t ^{2} + 7})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d t} ( ( 5 t - 3 ) ^{7} ) ( 8 t ^{2} + 7 ) - \frac{d}{d t} ( 8 t ^{2} + 7 ) ( 5 t - 3 ) ^{7}}{( 8 t ^{2} + 7 ) ^{2}}

\frac{d}{d t} ((5 t - 3)^{7}) = 35 (5 t - 3)^{6}

\frac{d}{d t} (8 t^{2} + 7) = 16 t

= \frac{35 ( 5 t - 3 ) ^{6} ( 8 t ^{2} + 7 ) - 16 t ( 5 t - 3 ) ^{7}}{( 8 t ^{2} + 7 ) ^{2}}

\frac{d}{d x} (\frac{2 x}{x ^{2} - 4})

\frac{d}{d x} (5^{c o s (x)} + ln (x^{2} + 1))

\int \frac{1}{y ( 100 - y )} d y

x \to 0 + lim (\frac{1}{1 - e ^{x}})

(\frac{2 x - 7}{2 + 3 x})

What is the derivative of ((5t-3)^7)/(8t^2+7) ?
The derivative of ((5t-3)^7)/(8t^2+7) is (35(5t-3)^6(8t^2+7)-16t(5t-3)^7)/((8t^2+7)^2)
What is the first derivative of ((5t-3)^7)/(8t^2+7) ?
The first derivative of ((5t-3)^7)/(8t^2+7) is (35(5t-3)^6(8t^2+7)-16t(5t-3)^7)/((8t^2+7)^2)