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

The derivative of (8(2x^4+5)^3) is 1536x^3(128x^4+5)^2

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

The first derivative of (8(2x^4+5)^3) is 1536x^3(128x^4+5)^2

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\frac{d}{d x} ((8 (2 x)^{4} + 5)^{3})

1536 x^{3} (128 x^{4} + 5)^{2}

Solution steps

\frac{d}{d x} ((8 (2 x)^{4} + 5)^{3})

Simplify

(8 (2 x)^{4} + 5)^{3} : (128 x^{4} + 5)^{3}

= \frac{d}{d x} ((128 x^{4} + 5)^{3})

Apply the chain rule:

3 (128 x^{4} + 5)^{2} \frac{d}{d x} (128 x^{4} + 5)

= 3 (128 x^{4} + 5)^{2} \frac{d}{d x} (128 x^{4} + 5)

\frac{d}{d x} (128 x^{4} + 5) = 512 x^{3}

= 3 (128 x^{4} + 5)^{2} \cdot 512 x^{3}

Simplify

= 1536 x^{3} (128 x^{4} + 5)^{2}

2 x^{3} - 3 x^{2} + 5

x^{^{'}} = 2 x

\frac{d y}{d t} - y = 2 cos (k t), y (0) = 7

\frac{d y}{d t} = \frac{( 4 t + y )}{4 y - t}

\frac{d y}{d x} = 1 + x^{2} + y^{2} + x^{2} y^{2}

What is the derivative of (8(2x^4+5)^3) ?
The derivative of (8(2x^4+5)^3) is 1536x^3(128x^4+5)^2
What is the first derivative of (8(2x^4+5)^3) ?
The first derivative of (8(2x^4+5)^3) is 1536x^3(128x^4+5)^2