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

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.

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 \(-3 \sin x\).

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

Final Answer