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Popular >

derivative of e^{cos(3x^2+x)}

Solution

derivative of

e^{c o s (3 x^{2} + x)}

Solution

- e^{c o s (3 x^{2} + x)} sin (3 x^{2} + x) (6 x + 1)

Solution steps

\frac{d}{d x} (e^{c o s (3 x^{2} + x)})

Apply the chain rule:

e^{c o s (3 x^{2} + x)} \frac{d}{d x} (cos (3 x^{2} + x))

= e^{c o s (3 x^{2} + x)} \frac{d}{d x} (cos (3 x^{2} + x))

\frac{d}{d x} (cos (3 x^{2} + x)) = - sin (3 x^{2} + x) (6 x + 1)

= e^{c o s (3 x^{2} + x)} (- sin (3 x^{2} + x) (6 x + 1))

Simplify

= - e^{c o s (3 x^{2} + x)} sin (3 x^{2} + x) (6 x + 1)

Popular Examples

derivative of ((x^2-3^3)/(x^2+2))

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

derivative of (3x/x)

\frac{d}{d x} (\frac{3 x}{x})

tangent of f(x)=(sqrt(2))^x,\at x=6 tangent of

f (x) = (2)^{x}, at x = 6

tangent of y=e^{6x}cos(pix),(0,1)tangent of

y = e^{6 x} cos (π x), (0, 1)

y^{''}+14y^'+28y=6675e^{2t}cos(15t)

y^{^{''}} + 14 y^{^{'}} + 28 y = 6675 e^{2 t} cos (15 t)

Frequently Asked Questions (FAQ)

What is the derivative of e^{cos(3x^2+x)} ?
The derivative of e^{cos(3x^2+x)} is -e^{cos(3x^2+x)}sin(3x^2+x)(6x+1)
What is the first derivative of e^{cos(3x^2+x)} ?
The first derivative of e^{cos(3x^2+x)} is -e^{cos(3x^2+x)}sin(3x^2+x)(6x+1)