What is the derivative of x+x^2+sqrt(x)+6/(7x^3) ?

The derivative of x+x^2+sqrt(x)+6/(7x^3) is (7x^{7/2}-36+28x^5)/(14x^{7/2)sqrt(x)}+1

What is the first derivative of x+x^2+sqrt(x)+6/(7x^3) ?

The first derivative of x+x^2+sqrt(x)+6/(7x^3) is (7x^{7/2}-36+28x^5)/(14x^{7/2)sqrt(x)}+1

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\frac{d}{d x} (x + x^{2} + x + \frac{6}{7 x ^{3}})

\frac{7 x ^{\frac{7}{2}} - 36 + 28 x ^{5}}{14 x ^{\frac{7}{2}} x} + 1

Solution steps

\frac{d}{d x} (x + x^{2} + x + \frac{6}{7 x ^{3}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d x}{d x} + \frac{d}{d x} (x^{2}) + \frac{d}{d x} (x) + \frac{d}{d x} (\frac{6}{7 x ^{3}})

\frac{d x}{d x} = 1

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (x) = \frac{1}{2 x}

\frac{d}{d x} (\frac{6}{7 x ^{3}}) = - \frac{18}{7 x ^{4}}

= 1 + 2 x + \frac{1}{2 x} - \frac{18}{7 x ^{4}}

Combine the fractions

\frac{1}{2 x} - \frac{18}{7 x ^{4}} + 2 x : \frac{7 x ^{\frac{7}{2}} - 36 + 28 x ^{5}}{14 x ^{\frac{7}{2}} x}

= \frac{7 x ^{\frac{7}{2}} - 36 + 28 x ^{5}}{14 x ^{\frac{7}{2}} x} + 1

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

\int cos^{5} (4 x) sin (4 x) d x

\frac{d}{d x} (ln (6 x^{2} + 2 x + 2))

\frac{d}{d t} (e^{\frac{t}{7}} cos (\frac{t}{7}))

\frac{d}{d x} (\frac{2 ^{x}}{e ^{x}})

What is the derivative of x+x^2+sqrt(x)+6/(7x^3) ?
The derivative of x+x^2+sqrt(x)+6/(7x^3) is (7x^{7/2}-36+28x^5)/(14x^{7/2)sqrt(x)}+1
What is the first derivative of x+x^2+sqrt(x)+6/(7x^3) ?
The first derivative of x+x^2+sqrt(x)+6/(7x^3) is (7x^{7/2}-36+28x^5)/(14x^{7/2)sqrt(x)}+1