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Popular >

derivative of sin^2(mx+ny(x))

Solution

\frac{d}{d x} (sin^{2} (m x + n y (x)))

Solution

2 sin (m x + n y (x)) cos (m x + n y (x)) (m + n \frac{d}{d x} (y (x)))

Solution steps

\frac{d}{d x} (sin^{2} (m x + n y (x)))

Apply the chain rule:

2 sin (m x + n y (x)) \frac{d}{d x} (sin (m x + n y (x)))

= 2 sin (m x + n y (x)) \frac{d}{d x} (sin (m x + n y (x)))

\frac{d}{d x} (sin (m x + n y (x))) = cos (m x + n y (x)) (m + n \frac{d}{d x} (y (x)))

= 2 sin (m x + n y (x)) cos (m x + n y (x)) (m + n \frac{d}{d x} (y (x)))

Popular Examples

t^2y^{''}-2ty^'+2y=tln(t)

t^{2} y^{^{''}} - 2 t y^{^{'}} + 2 y = t ln (t)

tangent of x^2+xy+y^2=7,(2,1)tangent of

x^{2} + x y + y^{2} = 7, (2, 1)

derivative of 4x^5-3x^m+2x^n+5x^2-x-6

\frac{d}{d x} (4 x^{5} - 3 x^{m} + 2 x^{n} + 5 x^{2} - x - 6)

(\partial)/(\partial x)(3y^2+12xy)

\frac{\partial}{\partial x} (3 y^{2} + 12 x y)

y^{^{'}} = 3 y^{2} e^{x} - 2 y

Frequently Asked Questions (FAQ)

What is the derivative of sin^2(mx+ny(x)) ?
The derivative of sin^2(mx+ny(x)) is 2sin(mx+n{y}(x))cos(mx+n{y}(x))(m+n derivative of {y}(x))
What is the first derivative of sin^2(mx+ny(x)) ?
The first derivative of sin^2(mx+ny(x)) is 2sin(mx+n{y}(x))cos(mx+n{y}(x))(m+n derivative of {y}(x))