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Popular >

derivative of sin(cos(x^2+3))

Solution

\frac{d}{d x} (sin (cos (x^{2} + 3)))

Solution

- 2 x cos (cos (x^{2} + 3)) sin (x^{2} + 3)

Solution steps

\frac{d}{d x} (sin (cos (x^{2} + 3)))

Apply the chain rule:

cos (cos (x^{2} + 3)) \frac{d}{d x} (cos (x^{2} + 3))

= cos (cos (x^{2} + 3)) \frac{d}{d x} (cos (x^{2} + 3))

\frac{d}{d x} (cos (x^{2} + 3)) = - sin (x^{2} + 3) \cdot 2 x

= cos (cos (x^{2} + 3)) (- sin (x^{2} + 3) \cdot 2 x)

Simplify

= - 2 x cos (cos (x^{2} + 3)) sin (x^{2} + 3)

Popular Examples

area y=4x,y=x^3+3x^2 area

y = 4 x, y = x^{3} + 3 x^{2}

integral from 0 to 1 of 2/7 x^2(x+3)

\int_{0}^{1} \frac{2}{7} x^{2} (x + 3) d x

integral from 0 to 1 of pi(5x^6-5x)^2

\int_{0}^{1} π (5 x^{6} - 5 x)^{2} d x

integral from 0 to 10 of xe^{-x}

\int_{0}^{10} x e^{- x} d x

xyy^'+y^2=xe^{-x}

x y y^{^{'}} + y^{2} = x e^{- x}

Frequently Asked Questions (FAQ)

What is the derivative of sin(cos(x^2+3)) ?
The derivative of sin(cos(x^2+3)) is -2xcos(cos(x^2+3))sin(x^2+3)
What is the first derivative of sin(cos(x^2+3)) ?
The first derivative of sin(cos(x^2+3)) is -2xcos(cos(x^2+3))sin(x^2+3)