What is the derivative of 7x^3-6sqrt(x)+3/(x^7)+9 ?

The derivative of 7x^3-6sqrt(x)+3/(x^7)+9 is (3(7x^{10}-x^{15/2}-7))/(x^8)

What is the first derivative of 7x^3-6sqrt(x)+3/(x^7)+9 ?

The first derivative of 7x^3-6sqrt(x)+3/(x^7)+9 is (3(7x^{10}-x^{15/2}-7))/(x^8)

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derivative of

7 x^{3} - 6 x + \frac{3}{x ^{7}} + 9

\frac{3 ( 7 x ^{10} - x ^{\frac{15}{2}} - 7 )}{x ^{8}}

Solution steps

\frac{d}{d x} (7 x^{3} - 6 x + \frac{3}{x ^{7}} + 9)

Simplify

7 x^{3} - 6 x + \frac{3}{x ^{7}} + 9 : \frac{3 + 7 x ^{10} - 6 x ^{\frac{15}{2}}}{x ^{7}} + 9

= \frac{d}{d x} (\frac{3 + 7 x ^{10} - 6 x ^{\frac{15}{2}}}{x ^{7}} + 9)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{3 + 7 x ^{10} - 6 x ^{\frac{15}{2}}}{x ^{7}}) + \frac{d}{d x} (9)

\frac{d}{d x} (\frac{3 + 7 x ^{10} - 6 x ^{\frac{15}{2}}}{x ^{7}}) = \frac{3 ( 7 x ^{10} - x ^{\frac{15}{2}} - 7 )}{x ^{8}}

\frac{d}{d x} (9) = 0

= \frac{3 ( 7 x ^{10} - x ^{\frac{15}{2}} - 7 )}{x ^{8}} + 0

Simplify

= \frac{3 ( 7 x ^{10} - x ^{\frac{15}{2}} - 7 )}{x ^{8}}

x \to + (- 4) lim (x^{2} - 3)

\int_{1}^{4} \frac{x - 3}{x} d x

f (x) = e^{x^{2} + 5 x}

\int_{0}^{π} sin^{2} (θ) d θ

n \to \infty lim (x + \frac{x}{n})

What is the derivative of 7x^3-6sqrt(x)+3/(x^7)+9 ?
The derivative of 7x^3-6sqrt(x)+3/(x^7)+9 is (3(7x^{10}-x^{15/2}-7))/(x^8)
What is the first derivative of 7x^3-6sqrt(x)+3/(x^7)+9 ?
The first derivative of 7x^3-6sqrt(x)+3/(x^7)+9 is (3(7x^{10}-x^{15/2}-7))/(x^8)