What is the derivative of x^2(x+1e^{k(x)}) ?

The derivative of x^2(x+1e^{k(x)}) is ke^{kx}x^3+ke^{kx}x^2+3e^{kx}x^2+2e^{kx}x

What is the first derivative of x^2(x+1e^{k(x)}) ?

The first derivative of x^2(x+1e^{k(x)}) is ke^{kx}x^3+ke^{kx}x^2+3e^{kx}x^2+2e^{kx}x

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\frac{d}{d x} (x^{2} (x + 1) e^{k (x)})

k e^{k x} x^{3} + k e^{k x} x^{2} + 3 e^{k x} x^{2} + 2 e^{k x} x

Solution steps

\frac{d}{d x} (x^{2} (x + 1) e^{k (x)})

Apply the Product Rule:

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

f = x^{2}, g = (x + 1) e^{k x}

= \frac{d}{d x} (x^{2}) (x + 1) e^{k x} + \frac{d}{d x} ((x + 1) e^{k x}) x^{2}

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

\frac{d}{d x} ((x + 1) e^{k x}) = e^{k x} + k e^{k x} (x + 1)

= 2 x (x + 1) e^{k x} + (e^{k x} + k e^{k x} (x + 1)) x^{2}

Simplify

2 x (x + 1) e^{k x} + (e^{k x} + k e^{k x} (x + 1)) x^{2} : k e^{k x} x^{3} + k e^{k x} x^{2} + 3 e^{k x} x^{2} + 2 e^{k x} x

= k e^{k x} x^{3} + k e^{k x} x^{2} + 3 e^{k x} x^{2} + 2 e^{k x} x

\frac{d y}{d t} = (y^{2} + 1) t

\frac{d}{d x} (10 + x)

\int_{0}^{1} \frac{51}{4 y - 1} d y

x \to 0 lim (\frac{2}{x} - \frac{2}{x ^{2} - x})

\frac{\partial}{\partial x} (x y^{2} z^{2})

What is the derivative of x^2(x+1e^{k(x)}) ?
The derivative of x^2(x+1e^{k(x)}) is ke^{kx}x^3+ke^{kx}x^2+3e^{kx}x^2+2e^{kx}x
What is the first derivative of x^2(x+1e^{k(x)}) ?
The first derivative of x^2(x+1e^{k(x)}) is ke^{kx}x^3+ke^{kx}x^2+3e^{kx}x^2+2e^{kx}x