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Popular >

derivative of sinh^3(xsin^2(x))

Solution

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

Solution

3 sinh^{2} (x) cosh (x) sin^{2} (x) + sin (2 x) sinh^{3} (x)

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sinh^{3} (x), g = sin^{2} (x)

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

\frac{d}{d x} (sinh^{3} (x)) = 3 sinh^{2} (x) cosh (x)

\frac{d}{d x} (sin^{2} (x)) = sin (2 x)

= 3 sinh^{2} (x) cosh (x) sin^{2} (x) + sin (2 x) sinh^{3} (x)

Graph

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n \to 1 lim (3 - \frac{7}{4 ^{n}})

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\frac{\partial}{\partial x} (x y^{10} + x^{2} + y^{4})

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\int (e^{3 x} + 1) d x

Frequently Asked Questions (FAQ)

What is the derivative of sinh^3(xsin^2(x)) ?
The derivative of sinh^3(xsin^2(x)) is 3sinh^2(x)cosh(x)sin^2(x)+sin(2x)sinh^3(x)
What is the first derivative of sinh^3(xsin^2(x)) ?
The first derivative of sinh^3(xsin^2(x)) is 3sinh^2(x)cosh(x)sin^2(x)+sin(2x)sinh^3(x)