What is the derivative of 1/(2sqrt(r)+7^{6/7)} ?

The derivative of 1/(2sqrt(r)+7^{6/7)} is -1/(r^{1/2)(2sqrt(r)+7^{6/7})^2}

What is the first derivative of 1/(2sqrt(r)+7^{6/7)} ?

The first derivative of 1/(2sqrt(r)+7^{6/7)} is -1/(r^{1/2)(2sqrt(r)+7^{6/7})^2}

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derivative of

\frac{1}{2 r + 7 ^{\frac{6}{7}}}

- \frac{1}{r ^{\frac{1}{2}} ( 2 r + 7 ^{\frac{6}{7}} ) ^{2}}

Solution steps

\frac{d}{d r} (\frac{1}{2 r + 7 ^{\frac{6}{7}}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{d}{d r} ((2 r + 7^{\frac{6}{7}})^{- 1})

Apply the chain rule:

- \frac{1}{( 2 r + 7 ^{\frac{6}{7}} ) ^{2}} \frac{d}{d r} (2 r + 7^{\frac{6}{7}})

= - \frac{1}{( 2 r + 7 ^{\frac{6}{7}} ) ^{2}} \frac{d}{d r} (2 r + 7^{\frac{6}{7}})

\frac{d}{d r} (2 r + 7^{\frac{6}{7}}) = \frac{1}{r ^{\frac{1}{2}}}

= - \frac{1}{( 2 r + 7 ^{\frac{6}{7}} ) ^{2}} \cdot \frac{1}{r ^{\frac{1}{2}}}

Simplify

- \frac{1}{( 2 r + 7 ^{\frac{6}{7}} ) ^{2}} \cdot \frac{1}{r ^{\frac{1}{2}}} : - \frac{1}{r ^{\frac{1}{2}} ( 2 r + 7 ^{\frac{6}{7}} ) ^{2}}

= - \frac{1}{r ^{\frac{1}{2}} ( 2 r + 7 ^{\frac{6}{7}} ) ^{2}}

\frac{d}{d x} (3 sin (1 + cos (4) x^{2}))

\int_{0}^{t} t^{2} e^{- \frac{t}{3}} d t

y = \frac{5}{x}, (5, 1)

\int_{1}^{8} (\frac{2}{x}) d x

f (x) = x^{3}, at x = 3

What is the derivative of 1/(2sqrt(r)+7^{6/7)} ?
The derivative of 1/(2sqrt(r)+7^{6/7)} is -1/(r^{1/2)(2sqrt(r)+7^{6/7})^2}
What is the first derivative of 1/(2sqrt(r)+7^{6/7)} ?
The first derivative of 1/(2sqrt(r)+7^{6/7)} is -1/(r^{1/2)(2sqrt(r)+7^{6/7})^2}