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Popular >

derivative of sin^4(x+cos^4(x))

Solution

\frac{d}{d x} (sin^{4} (x) + cos^{4} (x))

Solution

- 4 cos (x) sin (x) cos (2 x)

Solution steps

\frac{d}{d x} (sin^{4} (x) + cos^{4} (x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (sin^{4} (x)) + \frac{d}{d x} (cos^{4} (x))

\frac{d}{d x} (sin^{4} (x)) = 4 sin^{3} (x) cos (x)

\frac{d}{d x} (cos^{4} (x)) = - 4 cos^{3} (x) sin (x)

= 4 sin^{3} (x) cos (x) - 4 cos^{3} (x) sin (x)

Simplify

4 sin^{3} (x) cos (x) - 4 cos^{3} (x) sin (x) : - 4 cos (x) sin (x) cos (2 x)

= - 4 cos (x) sin (x) cos (2 x)

Popular Examples

laplacetransform 2cos(2t)laplace transform

2 cos (2 t)

y^{''}+8y^'+25y=0,y(3319)=-3,y^'(3319)=1

y^{^{''}} + 8 y^{^{'}} + 25 y = 0, y (3319) = - 3, y^{^{'}} (3319) = 1

integral of 1/((x^2-a^2))

\int \frac{1}{( x ^{2} - a ^{2} )} d x

derivative of x^2(20-x^3)

\frac{d}{d x} (x^{2} (20 - x)^{3})

integral of (5x+6)/((x-2)(3x+1)^2)

\int \frac{5 x + 6}{( x - 2 ) ( 3 x + 1 ) ^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of sin^4(x+cos^4(x)) ?
The derivative of sin^4(x+cos^4(x)) is -4cos(x)sin(x)cos(2x)
What is the first derivative of sin^4(x+cos^4(x)) ?
The first derivative of sin^4(x+cos^4(x)) is -4cos(x)sin(x)cos(2x)