What is the derivative of sqrt(7t^7+9) ?

The derivative of sqrt(7t^7+9) is (49t^6)/(2sqrt(7t^7+9))

What is the first derivative of sqrt(7t^7+9) ?

The first derivative of sqrt(7t^7+9) is (49t^6)/(2sqrt(7t^7+9))

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derivative of

7 t^{7} + 9

\frac{49 t ^{6}}{2 7 t ^{7} + 9}

Solution steps

\frac{d}{d t} (7 t^{7} + 9)

Apply the chain rule:

\frac{1}{2 7 t ^{7} + 9} \frac{d}{d t} (7 t^{7} + 9)

= \frac{1}{2 7 t ^{7} + 9} \frac{d}{d t} (7 t^{7} + 9)

\frac{d}{d t} (7 t^{7} + 9) = 49 t^{6}

= \frac{1}{2 7 t ^{7} + 9} \cdot 49 t^{6}

Simplify

\frac{1}{2 7 t ^{7} + 9} \cdot 49 t^{6} : \frac{49 t ^{6}}{2 7 t ^{7} + 9}

= \frac{49 t ^{6}}{2 7 t ^{7} + 9}

x^{- m}

\int \frac{1}{6 x - x ^{2}} d x

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What is the derivative of sqrt(7t^7+9) ?
The derivative of sqrt(7t^7+9) is (49t^6)/(2sqrt(7t^7+9))
What is the first derivative of sqrt(7t^7+9) ?
The first derivative of sqrt(7t^7+9) is (49t^6)/(2sqrt(7t^7+9))