What is the derivative of x^2sinh(2x) ?

The derivative of x^2sinh(2x) is 2xsinh(2x)+cosh(2x)*2x^2

What is the first derivative of x^2sinh(2x) ?

The first derivative of x^2sinh(2x) is 2xsinh(2x)+cosh(2x)*2x^2

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

2 x sinh (2 x) + cosh (2 x) \cdot 2 x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

= 2 x sinh (2 x) + cosh (2 x) \cdot 2 x^{2}

\int_{- π}^{π} e^{x} sin (n x) d x

\int \frac{sin ( 2 x )}{49 + cos ^{2} ( x )} d x

\frac{d}{d t} (t^{3} + 3 t)

\frac{\partial}{\partial x} (y tan (x))

\int \frac{e ^{x} + 1}{e ^{x} + x} d x

What is the derivative of x^2sinh(2x) ?
The derivative of x^2sinh(2x) is 2xsinh(2x)+cosh(2x)*2x^2
What is the first derivative of x^2sinh(2x) ?
The first derivative of x^2sinh(2x) is 2xsinh(2x)+cosh(2x)*2x^2