What is the derivative of f(x)=(7x^2+6)(5x+8+7/x) ?

The derivative of f(x)=(7x^2+6)(5x+8+7/x) is 105x^2+112x-(42)/(x^2)+79

What is the first derivative of f(x)=(7x^2+6)(5x+8+7/x) ?

The first derivative of f(x)=(7x^2+6)(5x+8+7/x) is 105x^2+112x-(42)/(x^2)+79

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derivative of

f (x) = (7 x^{2} + 6) (5 x + 8 + \frac{7}{x})

105 x^{2} + 112 x - \frac{42}{x ^{2}} + 79

Solution steps

\frac{d}{d x} ((7 x^{2} + 6) (5 x + 8 + \frac{7}{x}))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 7 x^{2} + 6, g = 5 x + 8 + \frac{7}{x}

= \frac{d}{d x} (7 x^{2} + 6) (5 x + 8 + \frac{7}{x}) + \frac{d}{d x} (5 x + 8 + \frac{7}{x}) (7 x^{2} + 6)

\frac{d}{d x} (7 x^{2} + 6) = 14 x

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

= 14 x (5 x + 8 + \frac{7}{x}) + (- \frac{7}{x ^{2}} + 5) (7 x^{2} + 6)

Simplify

14 x (5 x + 8 + \frac{7}{x}) + (- \frac{7}{x ^{2}} + 5) (7 x^{2} + 6) : 105 x^{2} + 112 x - \frac{42}{x ^{2}} + 79

= 105 x^{2} + 112 x - \frac{42}{x ^{2}} + 79

sin^{2} (y)

\int \frac{sin ^{3} ( x )}{1 - cos ( x )} d x

\int x - \frac{1}{x} d x

\int (e^{2 x} cos (e^{2 x})) d x

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

What is the derivative of f(x)=(7x^2+6)(5x+8+7/x) ?
The derivative of f(x)=(7x^2+6)(5x+8+7/x) is 105x^2+112x-(42)/(x^2)+79
What is the first derivative of f(x)=(7x^2+6)(5x+8+7/x) ?
The first derivative of f(x)=(7x^2+6)(5x+8+7/x) is 105x^2+112x-(42)/(x^2)+79