What is the derivative of 2(x^2+5x-2^{-5/7}) ?

The derivative of 2(x^2+5x-2^{-5/7}) is -(10(2x+5))/(7(x^2+5x-2)^{12/7)}

What is the first derivative of 2(x^2+5x-2^{-5/7}) ?

The first derivative of 2(x^2+5x-2^{-5/7}) is -(10(2x+5))/(7(x^2+5x-2)^{12/7)}

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\frac{d}{d x} (2 (x^{2} + 5 x - 2)^{- \frac{5}{7}})

- \frac{10 ( 2 x + 5 )}{7 ( x ^{2} + 5 x - 2 ) ^{\frac{12}{7}}}

Solution steps

\frac{d}{d x} (2 (x^{2} + 5 x - 2)^{- \frac{5}{7}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} ((x^{2} + 5 x - 2)^{- \frac{5}{7}})

Apply the chain rule:

- \frac{5}{7 ( x ^{2} + 5 x - 2 ) ^{\frac{12}{7}}} \frac{d}{d x} (x^{2} + 5 x - 2)

= - \frac{5}{7 ( x ^{2} + 5 x - 2 ) ^{\frac{12}{7}}} \frac{d}{d x} (x^{2} + 5 x - 2)

\frac{d}{d x} (x^{2} + 5 x - 2) = 2 x + 5

= 2 (- \frac{5}{7 ( x ^{2} + 5 x - 2 ) ^{\frac{12}{7}}} (2 x + 5))

Simplify

2 (- \frac{5}{7 ( x ^{2} + 5 x - 2 ) ^{\frac{12}{7}}} (2 x + 5)) : - \frac{10 ( 2 x + 5 )}{7 ( x ^{2} + 5 x - 2 ) ^{\frac{12}{7}}}

= - \frac{10 ( 2 x + 5 )}{7 ( x ^{2} + 5 x - 2 ) ^{\frac{12}{7}}}

What is the derivative of 2(x^2+5x-2^{-5/7}) ?
The derivative of 2(x^2+5x-2^{-5/7}) is -(10(2x+5))/(7(x^2+5x-2)^{12/7)}
What is the first derivative of 2(x^2+5x-2^{-5/7}) ?
The first derivative of 2(x^2+5x-2^{-5/7}) is -(10(2x+5))/(7(x^2+5x-2)^{12/7)}