Solved: "find dydx f(x)=x2sin⁡(x)"

High School
Calculus and Analysis
Calculus 1
Derivatives

emancipezN

Answered question

2021-06-08

find $\frac{d y}{d x}$
$f (x) = x^{2} \sin (x)$

Answer & Explanation

unett

Skilled2021-06-09Added 119 answers

Step 1
We have to find derivative of f(x) where f(x) is given by:
$\Rightarrow \cdot f (x) = x^{2} \sin x$
$\Rightarrow \cdot f^{'} (x) = ?$
Step 2
We will use following rules to find derivatives.
$\Rightarrow \cdot$ power rule: $\frac{d}{d x} [x^{n}] = n x^{n - 1}$
$\Rightarrow \cdot$ product rule: $\frac{\partial}{\partial x} (u v) = \frac{\partial u}{\partial x} v + u \frac{\partial v}{\partial x}$
Step 3
With the help of power rule and product rule we will find f'(x) work is shown below:
$\Rightarrow \cdot f (x) = x^{2} \sin x$
$\Rightarrow \cdot f^{'} (x) = 2 x \sin x + x^{2} \cos x$
Step 4
Answer
$\Rightarrow \cdot f^{'} (x) = 2 x \sin x + x^{2} \cos x$

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