What is the derivative of f(x)=xe^{4x+sin(x)-10} ?

The derivative of f(x)=xe^{4x+sin(x)-10} is e^{4x+sin(x)-10}+e^{4x+sin(x)-10}x(cos(x)+4)

What is the first derivative of f(x)=xe^{4x+sin(x)-10} ?

The first derivative of f(x)=xe^{4x+sin(x)-10} is e^{4x+sin(x)-10}+e^{4x+sin(x)-10}x(cos(x)+4)

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derivative of

f (x) = x e^{4 x + s i n (x) - 10}

e^{4 x + s i n (x) - 10} + e^{4 x + s i n (x) - 10} x (cos (x) + 4)

Solution steps

\frac{d}{d x} (x e^{4 x + s i n (x) - 10})

Apply the Product Rule:

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

f = x, g = e^{4 x + s i n (x) - 10}

= \frac{d x}{d x} e^{4 x + s i n (x) - 10} + \frac{d}{d x} (e^{4 x + s i n (x) - 10}) x

\frac{d x}{d x} = 1

\frac{d}{d x} (e^{4 x + s i n (x) - 10}) = e^{4 x + s i n (x) - 10} (cos (x) + 4)

= 1 \cdot e^{4 x + s i n (x) - 10} + e^{4 x + s i n (x) - 10} (cos (x) + 4) x

Simplify

= e^{4 x + s i n (x) - 10} + e^{4 x + s i n (x) - 10} x (cos (x) + 4)

\frac{\partial}{\partial x} (2 e^{x yz} sin (x w))

\int_{2}^{5} \frac{1}{x} d x

x^{2} - 1

\int_{1}^{4} 8 x ln (x) d x

\int (x^{3} + 4 x y) d x

What is the derivative of f(x)=xe^{4x+sin(x)-10} ?
The derivative of f(x)=xe^{4x+sin(x)-10} is e^{4x+sin(x)-10}+e^{4x+sin(x)-10}x(cos(x)+4)
What is the first derivative of f(x)=xe^{4x+sin(x)-10} ?
The first derivative of f(x)=xe^{4x+sin(x)-10} is e^{4x+sin(x)-10}+e^{4x+sin(x)-10}x(cos(x)+4)