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

The derivative of 7+2x+x^3(5x^2+1)^5 is 50x^4(5x^2+1)^4+3x^2(5x^2+1)^5+2

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

The first derivative of 7+2x+x^3(5x^2+1)^5 is 50x^4(5x^2+1)^4+3x^2(5x^2+1)^5+2

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derivative of

7 + 2 x + x^{3} (5 x^{2} + 1)^{5}

50 x^{4} (5 x^{2} + 1)^{4} + 3 x^{2} (5 x^{2} + 1)^{5} + 2

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (7) = 0

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

\frac{d}{d x} (x^{3} (5 x^{2} + 1)^{5}) = 3 x^{2} (5 x^{2} + 1)^{5} + 50 x^{4} (5 x^{2} + 1)^{4}

= 0 + 2 + 3 x^{2} (5 x^{2} + 1)^{5} + 50 x^{4} (5 x^{2} + 1)^{4}

Simplify

= 50 x^{4} (5 x^{2} + 1)^{4} + 3 x^{2} (5 x^{2} + 1)^{5} + 2

x \to 0 lim (\frac{1}{3 x sin ( x )})

\frac{d}{d x} (ln (\frac{3 x ^{4} + 2}{4 x}))

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

6^{4 - x^{2}}

\frac{d}{d x} (\frac{2 - 3 x - x ^{2}}{x ^{2} - 4})

What is the derivative of 7+2x+x^3(5x^2+1)^5 ?
The derivative of 7+2x+x^3(5x^2+1)^5 is 50x^4(5x^2+1)^4+3x^2(5x^2+1)^5+2
What is the first derivative of 7+2x+x^3(5x^2+1)^5 ?
The first derivative of 7+2x+x^3(5x^2+1)^5 is 50x^4(5x^2+1)^4+3x^2(5x^2+1)^5+2