What is the derivative of 16^4sqrt(4x^4+4) ?

The derivative of 16^4sqrt(4x^4+4) is (262144x^3)/(sqrt(x^4+1))

What is the first derivative of 16^4sqrt(4x^4+4) ?

The first derivative of 16^4sqrt(4x^4+4) is (262144x^3)/(sqrt(x^4+1))

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derivative of

1 6^{4} 4 x^{4} + 4

\frac{262144 x ^{3}}{x ^{4} + 1}

Solution steps

\frac{d}{d x} (1 6^{4} 4 x^{4} + 4)

Simplify

1 6^{4} 4 x^{4} + 4 : 65536 4 x^{4} + 4

= \frac{d}{d x} (65536 4 x^{4} + 4)

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 65536 \frac{d}{d x} (4 x^{4} + 4)

Apply the chain rule:

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

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

\frac{d}{d x} (4 x^{4} + 4) = 16 x^{3}

= 65536 \cdot \frac{1}{2 4 x ^{4} + 4} \cdot 16 x^{3}

Simplify

65536 \cdot \frac{1}{2 4 x ^{4} + 4} \cdot 16 x^{3} : \frac{262144 x ^{3}}{x ^{4} + 1}

= \frac{262144 x ^{3}}{x ^{4} + 1}

What is the derivative of 16^4sqrt(4x^4+4) ?
The derivative of 16^4sqrt(4x^4+4) is (262144x^3)/(sqrt(x^4+1))
What is the first derivative of 16^4sqrt(4x^4+4) ?
The first derivative of 16^4sqrt(4x^4+4) is (262144x^3)/(sqrt(x^4+1))