What is the derivative of 2x^3+1/(x^2+16x^{7/2}+5) ?

The derivative of 2x^3+1/(x^2+16x^{7/2}+5) is (2(3x^5+28x^{11/2}-1))/(x^3)

What is the first derivative of 2x^3+1/(x^2+16x^{7/2}+5) ?

The first derivative of 2x^3+1/(x^2+16x^{7/2}+5) is (2(3x^5+28x^{11/2}-1))/(x^3)

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\frac{d}{d x} (2 x^{3} + \frac{1}{x ^{2}} + 16 x^{\frac{7}{2}} + 5)

\frac{2 ( 3 x ^{5} + 28 x ^{\frac{11}{2}} - 1 )}{x ^{3}}

Solution steps

\frac{d}{d x} (2 x^{3} + \frac{1}{x ^{2}} + 16 x^{\frac{7}{2}} + 5)

Simplify

2 x^{3} + \frac{1}{x ^{2}} + 16 x^{\frac{7}{2}} + 5 : \frac{1 + 2 x ^{5} + 16 x ^{\frac{11}{2}}}{x ^{2}} + 5

= \frac{d}{d x} (\frac{1 + 2 x ^{5} + 16 x ^{\frac{11}{2}}}{x ^{2}} + 5)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{1 + 2 x ^{5} + 16 x ^{\frac{11}{2}}}{x ^{2}}) + \frac{d}{d x} (5)

\frac{d}{d x} (\frac{1 + 2 x ^{5} + 16 x ^{\frac{11}{2}}}{x ^{2}}) = \frac{2 ( 3 x ^{5} + 28 x ^{\frac{11}{2}} - 1 )}{x ^{3}}

\frac{d}{d x} (5) = 0

= \frac{2 ( 3 x ^{5} + 28 x ^{\frac{11}{2}} - 1 )}{x ^{3}} + 0

Simplify

= \frac{2 ( 3 x ^{5} + 28 x ^{\frac{11}{2}} - 1 )}{x ^{3}}

2 x y^{^{'}} + y = 6 x, y (4) = 20

x \to 6 - lim (\frac{x + 9}{x + 6})

x^{^{''''}} = 0

x \to 5 lim (x)

y^{^{''}} - y^{^{'}} - 6 y = 0, y^{^{'}} (0) = - 6

What is the derivative of 2x^3+1/(x^2+16x^{7/2}+5) ?
The derivative of 2x^3+1/(x^2+16x^{7/2}+5) is (2(3x^5+28x^{11/2}-1))/(x^3)
What is the first derivative of 2x^3+1/(x^2+16x^{7/2}+5) ?
The first derivative of 2x^3+1/(x^2+16x^{7/2}+5) is (2(3x^5+28x^{11/2}-1))/(x^3)