By examining the pattern of derivatives, determine the 500th \text{500th} derivative of 7 cos ⁡ ( 3 x ) 7\cos\left(3x\right) .

7 ⋅ 3 500 cos ⁡ ( 3 x ) 7\cdot3^{500}\cos\left(3x\right)

− 7 ⋅ 3 500 cos ⁡ ( 3 x ) -7\cdot3^{500}\cos\left(3x\right)

7 ⋅ 3 500 sin ⁡ ( 3 x ) 7\cdot3^{500}\sin\left(3x\right)

− 7 ⋅ 3 500 sin ⁡ ( 3 x ) -7\cdot3^{500}\sin\left(3x\right)

Higher Order Derivatives

3. Techniques of Differentiation / Higher Order Derivatives / Problem 3

Problem 3

By examining the pattern of derivatives, determine the $500 th$ derivative of $7 cosine 3 x$ .

$7 \cdot 3^{500} \cos (3 x)$

$- 7 \cdot 3^{500} \cos (3 x)$

$7 \cdot 3^{500} \sin (3 x)$

$- 7 \cdot 3^{500} \sin (3 x)$