Question

Differentiate y=3cos(5x^2+2x+sin4x)

Answer 1

Answer:

cos22x+(cos2x)2+(sin2x)2+(cos2x)3+(sin2x)3=2

45cos22x+(cos2x+sin2x)2−2sin2x⋅cos2x+(cos2x+sin2x)(sin4x+cos4x−sin2x⋅cos2x)=2

⇒45cos22x+1−2sin2x.cos2x+(sin4x+cos4x−sin2x⋅cos2x)=2

45cos22x+1−2sin2x.cos2x+(

Answer 2

Step-by-step explanation:

Given:

$y = 3 \cos(5 {x}^{2} + 2x + sin4x)$

To find: Differentiation of y.

Solution:

Tip:

$\boxed{\bf \frac{d}{dx} cos(f(x)) = -sin(f(x)).f(x)}$

Step 1: Do the differentiation of cos(f(x)).

According to the formula

$\frac{d}{dx}(3 \cos(5 {x}^{2} + 2x + sin4x)) = -3sin(5 {x}^{2} + 2x + sin4x)) . \frac{d}{dx} (5 {x}^{2} + 2x + sin4x)$

Step 2: Do differentiation of f(x)

$\frac{d}{dx}(3 \cos(5 {x}^{2} + 2x + sin4x)) = -3sin(5 {x}^{2} + 2x + sin4x)) . (10 {x} + 2 +4 cos4x)$

Final answer:

$\bf \frac{d}{dx}(3 \cos(5 {x}^{2} + 2x + sin4x)) = -3sin(5 {x}^{2} + 2x + sin4x)) . (10 {x} + 2 +4 cos4x)$

Hope it helps you.

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