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

The derivative of f(x)=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 f(x)=7+2x+x^3(5x^2+1)^5 ?

The first derivative of f(x)=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

f (x) = 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

\int - x cos (nπ x) d x

f (x) = x^{11} e^{x}

\frac{d}{d θ} (2 - sin (θ))

x e^{- x + 1}, at 1

y = \frac{- 2 x}{x ^{2} + 1}, (- 1, 1)

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