"Compute the derivatives of the functions g(x)=(x+x2)(x3+x+2)" was answered by students like you

College
Calculus and Analysis
Differential Calculus
Derivatives

Cheyanne Leigh

Answered question

2021-09-30

Compute the derivatives of the functions

g (x) = (\sqrt{x} + x^{2}) (x^{3} + x + \sqrt{2})

Answer & Explanation

comentezq

Skilled2021-10-01Added 106 answers

Step 1
Given
$g (x) = (\sqrt{x} + x^{2}) (x^{3} + x + \sqrt{2})$
To take derivative of $g (x)$ , we apply product rule
$(u v)^{'} = u^{'} v + v^{'} u$
$g (x) = (\sqrt{x} + x^{2}) (x^{3} + x + \sqrt{2})$
$u = \sqrt{x} + x^{2}$
$u^{'} = \frac{1}{2 \sqrt{x}} + 2 x$
$v = x^{3} + x + \sqrt{2}$
$v^{'} = 3 x^{2} + 1$
Step 2
Now we apply product rule
$g (x) = (\sqrt{x} + x^{2}) (x^{3} + x + \sqrt{2})$
$g^{'} (x) = (\frac{1}{2 \sqrt{x}} + 2 x) (x^{3} + x + \sqrt{2}) + (3 x^{2} + 1) (\sqrt{x} + x^{2})$

Jeffrey Jordon

Expert2022-02-01Added 2605 answers

Answer is given below (on video)

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