Questions: Calculate the derivative of h(x) = 2 sin x + 3 cos x.

Calculate the derivative of h(x) = 2 sin x + 3 cos x.
Transcript text: Question Calculate the derivative of $h(x)=2 \sin x+3 \cos x$. Select the correct answer below:
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Solution

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Solution Steps

To find the derivative of the function \( h(x) = 2 \sin x + 3 \cos x \), apply the basic differentiation rules for sine and cosine. The derivative of \(\sin x\) is \(\cos x\), and the derivative of \(\cos x\) is \(-\sin x\). Use these rules to differentiate each term separately.

Step 1: Differentiate Each Term

To find the derivative of \( h(x) = 2 \sin x + 3 \cos x \), differentiate each term separately:

  • The derivative of \( 2 \sin x \) is \( 2 \cos x \).
  • The derivative of \( 3 \cos x \) is \(-3 \sin x\).
Step 2: Combine the Derivatives

Combine the derivatives of each term to get the derivative of the entire function: \[ h'(x) = 2 \cos x - 3 \sin x \]

Final Answer

The derivative of \( h(x) = 2 \sin x + 3 \cos x \) is: \[ \boxed{h'(x) = 2 \cos x - 3 \sin x} \]

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