What is the derivative of (2x+1^4+8x(2x+1)^3) ?

The derivative of (2x+1^4+8x(2x+1)^3) is 320x^3+384x^2+144x+16

What is the first derivative of (2x+1^4+8x(2x+1)^3) ?

The first derivative of (2x+1^4+8x(2x+1)^3) is 320x^3+384x^2+144x+16

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\frac{d}{d x} ((2 x + 1)^{4} + 8 x (2 x + 1)^{3})

320 x^{3} + 384 x^{2} + 144 x + 16

Solution steps

\frac{d}{d x} ((2 x + 1)^{4} + 8 x (2 x + 1)^{3})

Simplify

(2 x + 1)^{4} + 8 x (2 x + 1)^{3} : 80 x^{4} + 128 x^{3} + 72 x^{2} + 16 x + 1

= \frac{d}{d x} (80 x^{4} + 128 x^{3} + 72 x^{2} + 16 x + 1)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (80 x^{4}) + \frac{d}{d x} (128 x^{3}) + \frac{d}{d x} (72 x^{2}) + \frac{d}{d x} (16 x) + \frac{d}{d x} (1)

\frac{d}{d x} (80 x^{4}) = 320 x^{3}

\frac{d}{d x} (128 x^{3}) = 384 x^{2}

\frac{d}{d x} (72 x^{2}) = 144 x

\frac{d}{d x} (16 x) = 16

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

= 320 x^{3} + 384 x^{2} + 144 x + 16 + 0

Simplify

= 320 x^{3} + 384 x^{2} + 144 x + 16

\int \frac{28 e ^{4 x}}{6 + e ^{4 x}} d x

t e^{10 t}

x \to 0 lim (\frac{( arctan ( 4 x ) )}{ln ( x )})

\frac{\partial}{\partial x} (ln (4 x + 5 y))

x \to 0 + lim (e^{- 2 x} ln (x))

What is the derivative of (2x+1^4+8x(2x+1)^3) ?
The derivative of (2x+1^4+8x(2x+1)^3) is 320x^3+384x^2+144x+16
What is the first derivative of (2x+1^4+8x(2x+1)^3) ?
The first derivative of (2x+1^4+8x(2x+1)^3) is 320x^3+384x^2+144x+16