What is the derivative of (2x+1^5+10x(2x+1)^4) ?

The derivative of (2x+1^5+10x(2x+1)^4) is 960x^4+1600x^3+960x^2+240x+20

What is the first derivative of (2x+1^5+10x(2x+1)^4) ?

The first derivative of (2x+1^5+10x(2x+1)^4) is 960x^4+1600x^3+960x^2+240x+20

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\frac{d}{d x} ((2 x + 1)^{5} + 10 x (2 x + 1)^{4})

960 x^{4} + 1600 x^{3} + 960 x^{2} + 240 x + 20

Solution steps

\frac{d}{d x} ((2 x + 1)^{5} + 10 x (2 x + 1)^{4})

Simplify

(2 x + 1)^{5} + 10 x (2 x + 1)^{4} : 192 x^{5} + 400 x^{4} + 320 x^{3} + 120 x^{2} + 20 x + 1

= \frac{d}{d x} (192 x^{5} + 400 x^{4} + 320 x^{3} + 120 x^{2} + 20 x + 1)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (192 x^{5}) + \frac{d}{d x} (400 x^{4}) + \frac{d}{d x} (320 x^{3}) + \frac{d}{d x} (120 x^{2}) + \frac{d}{d x} (20 x) + \frac{d}{d x} (1)

\frac{d}{d x} (192 x^{5}) = 960 x^{4}

\frac{d}{d x} (400 x^{4}) = 1600 x^{3}

\frac{d}{d x} (320 x^{3}) = 960 x^{2}

\frac{d}{d x} (120 x^{2}) = 240 x

\frac{d}{d x} (20 x) = 20

\frac{d}{d x} (1) = 0

= 960 x^{4} + 1600 x^{3} + 960 x^{2} + 240 x + 20 + 0

Simplify

= 960 x^{4} + 1600 x^{3} + 960 x^{2} + 240 x + 20

\frac{\partial}{\partial s} (2 s^{2} + t^{2})

\frac{\partial}{\partial s} (e^{s^{3} + t^{2}})

\frac{1}{4} y^{^{''}} + y^{^{'}} + y = x^{2} - 5 x

\int e^{x} x + e^{x} d x

f (x) = \frac{3}{2 x ^{5}}

What is the derivative of (2x+1^5+10x(2x+1)^4) ?
The derivative of (2x+1^5+10x(2x+1)^4) is 960x^4+1600x^3+960x^2+240x+20
What is the first derivative of (2x+1^5+10x(2x+1)^4) ?
The first derivative of (2x+1^5+10x(2x+1)^4) is 960x^4+1600x^3+960x^2+240x+20