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Popular >

derivative of y=sqrt(x)(x^4+1)

Solution

derivative of

y = x (x^{4} + 1)

Solution

\frac{9 x ^{4} + 1}{2 x}

Solution steps

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

Apply the Product Rule:

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

f = x, g = x^{4} + 1

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

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

Simplify

\frac{1}{2 x} (x^{4} + 1) + 4 x^{3} x : \frac{9 x ^{4} + 1}{2 x}

= \frac{9 x ^{4} + 1}{2 x}

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Frequently Asked Questions (FAQ)

What is the derivative of y=sqrt(x)(x^4+1) ?
The derivative of y=sqrt(x)(x^4+1) is (9x^4+1)/(2sqrt(x))
What is the first derivative of y=sqrt(x)(x^4+1) ?
The first derivative of y=sqrt(x)(x^4+1) is (9x^4+1)/(2sqrt(x))