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Popular Calculus >

derivative of f(x)=sqrt(7x^4+5)

Solution

derivative of

f (x) = 7 x^{4} + 5

Solution

\frac{14 x ^{3}}{7 x ^{4} + 5}

Solution steps

\frac{d}{d x} (7 x^{4} + 5)

Apply the chain rule:

\frac{1}{2 7 x ^{4} + 5} \frac{d}{d x} (7 x^{4} + 5)

= \frac{1}{2 7 x ^{4} + 5} \frac{d}{d x} (7 x^{4} + 5)

\frac{d}{d x} (7 x^{4} + 5) = 28 x^{3}

= \frac{1}{2 7 x ^{4} + 5} \cdot 28 x^{3}

Simplify

\frac{1}{2 7 x ^{4} + 5} \cdot 28 x^{3} : \frac{14 x ^{3}}{7 x ^{4} + 5}

= \frac{14 x ^{3}}{7 x ^{4} + 5}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=sqrt(7x^4+5) ?
The derivative of f(x)=sqrt(7x^4+5) is (14x^3)/(sqrt(7x^4+5))
What is the first derivative of f(x)=sqrt(7x^4+5) ?
The first derivative of f(x)=sqrt(7x^4+5) is (14x^3)/(sqrt(7x^4+5))