What is the derivative of 357x+45(x+1/x ^3) ?

The derivative of 357x+45(x+1/x ^3) is 135x^2+492-(135)/(x^2)-(135)/(x^4)

What is the first derivative of 357x+45(x+1/x ^3) ?

The first derivative of 357x+45(x+1/x ^3) is 135x^2+492-(135)/(x^2)-(135)/(x^4)

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\frac{d}{d x} (357 x + 45 (x + \frac{1}{x})^{3})

135 x^{2} + 492 - \frac{135}{x ^{2}} - \frac{135}{x ^{4}}

Solution steps

\frac{d}{d x} (357 x + 45 (x + \frac{1}{x})^{3})

Simplify

357 x + 45 (x + \frac{1}{x})^{3} : 45 x^{3} + 492 x + \frac{135}{x} + \frac{45}{x ^{3}}

= \frac{d}{d x} (45 x^{3} + 492 x + \frac{135}{x} + \frac{45}{x ^{3}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (45 x^{3}) + \frac{d}{d x} (492 x) + \frac{d}{d x} (\frac{135}{x}) + \frac{d}{d x} (\frac{45}{x ^{3}})

\frac{d}{d x} (45 x^{3}) = 135 x^{2}

\frac{d}{d x} (492 x) = 492

\frac{d}{d x} (\frac{135}{x}) = - \frac{135}{x ^{2}}

\frac{d}{d x} (\frac{45}{x ^{3}}) = - \frac{135}{x ^{4}}

= 135 x^{2} + 492 - \frac{135}{x ^{2}} - \frac{135}{x ^{4}}

(t - 1) (3 (t - 1)^{2} + 9 (t - 1) + 3)

\int \frac{1}{sec ( y )} d y

x \to 0 lim (x (sin (\frac{1}{x})))

\frac{d ^{2}}{d x ^{2}} (\frac{x}{x + 4})

\frac{\partial}{\partial x} (ln (y^{2} + x^{2}))

What is the derivative of 357x+45(x+1/x ^3) ?
The derivative of 357x+45(x+1/x ^3) is 135x^2+492-(135)/(x^2)-(135)/(x^4)
What is the first derivative of 357x+45(x+1/x ^3) ?
The first derivative of 357x+45(x+1/x ^3) is 135x^2+492-(135)/(x^2)-(135)/(x^4)