Question

If y=sin(x²+7) find Dy/Dx​

Answer 1

Answer:

$\frac{dy}{dx} = 2xcos(x^2+7)$

Step-by-step explanation:

Given: $y=sin(x^2+7)$

Find: $\frac{dy}{dx}$

For this problem, it looks like we are going to use the chain rule. We have to functions, let's label them:

$f(x)=sin(x)\\g(x)=x^2+7$

Let's remember that the chain rule is: $f'(g(x))*g'(x)$ or $(\frac{dy}{du} )(\frac{du}{dx} )$

Since these functions are basic, I will be using the $f'(g(x))*g'(x)$ rule, but both rules always work. We need to find $f'(x)$ and $g'(x)$

$f'(x)=cos(x)\\g'(x)=2x$

Remember that the derivative of $sin(x)$ is $cos(x)$. Make sure you know all your trig derivatives. Now that we know all our variables, we can plug them in. We will take $g(x)$ and plug it into $f'(x)$ and multiply it all by $g'(x)$.

$[cos(x^2+7)][2x]=2xcos(x^2+7)$

Since nothing else can be done to reduce this expression, your answer is:

$\frac{dy}{dx} = 2xcos(x^2+7)$

Answer 2

Answer  dy/dx = 2x cos (x to the second power + 7)

Step-by-step explanation: