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tatuchka [14]
3 years ago
14

PLEASE HELP! WILL MARK BRAINLIEST!

Mathematics
2 answers:
dedylja [7]3 years ago
5 0

Answer:

at first put the value of X

after that do the equation.

Step-by-step explanation:

hope it will help you

maria [59]3 years ago
5 0

Answer:

a = 2

Step-by-step explanation:

substitute x with the number 5.

5+8a=25+5a-7a

subtract 5a from both sides

5+3a=25-7a

add 7a to both sides

5+10a = 25

subtract 5 from both sides

10a=20

divide both sides by 10

a = 2

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How to find the derivative of cos^2x? i seem to be confused.
slamgirl [31]
If you're using the app, try seeing this answer through your browser:  brainly.com/question/2927231

————————

You can actually use either the product rule or the chain rule for this one. Observe:

•  Method I:

y = cos² x

y = cos x · cos x


Differentiate it by applying the product rule:

\mathsf{\dfrac{dy}{dx}=\dfrac{d}{dx}(cos\,x\cdot cos\,x)}\\\\\\
\mathsf{\dfrac{dy}{dx}=\dfrac{d}{dx}(cos\,x)\cdot cos\,x+cos\,x\cdot \dfrac{d}{dx}(cos\,x)}


The derivative of  cos x  is  – sin x. So you have

\mathsf{\dfrac{dy}{dx}=(-sin\,x)\cdot cos\,x+cos\,x\cdot (-sin\,x)}\\\\\\
\mathsf{\dfrac{dy}{dx}=-sin\,x\cdot cos\,x-cos\,x\cdot sin\,x}


\therefore~~\boxed{\begin{array}{c}\mathsf{\dfrac{dy}{dx}=-2\,sin\,x\cdot cos\,x}\end{array}}\qquad\quad\checkmark

—————

•  Method II:

You can also treat  y  as a composite function:

\left\{\!
\begin{array}{l}
\mathsf{y=u^2}\\\\
\mathsf{u=cos\,x}
\end{array}
\right.


and then, differentiate  y  by applying the chain rule:

\mathsf{\dfrac{dy}{dx}=\dfrac{dy}{du}\cdot \dfrac{du}{dx}}\\\\\\
\mathsf{\dfrac{dy}{dx}=\dfrac{d}{du}(u^2)\cdot \dfrac{d}{dx}(cos\,x)}


For that first derivative with respect to  u, just use the power rule, then you have

\mathsf{\dfrac{dy}{dx}=2u^{2-1}\cdot \dfrac{d}{dx}(cos\,x)}\\\\\\
\mathsf{\dfrac{dy}{dx}=2u\cdot (-sin\,x)\qquad\quad (but~~u=cos\,x)}\\\\\\
\mathsf{\dfrac{dy}{dx}=2\,cos\,x\cdot (-sin\,x)}


and then you get the same answer:

\therefore~~\boxed{\begin{array}{c}\mathsf{\dfrac{dy}{dx}=-2\,sin\,x\cdot cos\,x}\end{array}}\qquad\quad\checkmark


I hope this helps. =)


Tags:  <em>derivative chain rule product rule composite function trigonometric trig squared cosine cos differential integral calculus</em>

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