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

The derivative of (4x^2+5(5x+2)^4) is 8x(5x+2)^4+20(5x+2)^3(4x^2+5)

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

The first derivative of (4x^2+5(5x+2)^4) is 8x(5x+2)^4+20(5x+2)^3(4x^2+5)

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

8 x (5 x + 2)^{4} + 20 (5 x + 2)^{3} (4 x^{2} + 5)

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 4 x^{2} + 5, g = (5 x + 2)^{4}

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

\frac{d}{d x} (4 x^{2} + 5) = 8 x

\frac{d}{d x} ((5 x + 2)^{4}) = 20 (5 x + 2)^{3}

= 8 x (5 x + 2)^{4} + 20 (5 x + 2)^{3} (4 x^{2} + 5)

\frac{d}{d t} ((t - 1)^{2})

\frac{d}{d x} (3^{c o s (x)})

\int \frac{5}{7 + 5 x} d x

\frac{d}{d x} (x^{2} + A x + B)

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

What is the derivative of (4x^2+5(5x+2)^4) ?
The derivative of (4x^2+5(5x+2)^4) is 8x(5x+2)^4+20(5x+2)^3(4x^2+5)
What is the first derivative of (4x^2+5(5x+2)^4) ?
The first derivative of (4x^2+5(5x+2)^4) is 8x(5x+2)^4+20(5x+2)^3(4x^2+5)