What is the derivative of (x^3+2xe^{sin(x)}) ?

The derivative of (x^3+2xe^{sin(x)}) is (3x^2+2)e^{sin(x)}+e^{sin(x)}cos(x)(x^3+2x)

What is the first derivative of (x^3+2xe^{sin(x)}) ?

The first derivative of (x^3+2xe^{sin(x)}) is (3x^2+2)e^{sin(x)}+e^{sin(x)}cos(x)(x^3+2x)

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\frac{d}{d x} ((x^{3} + 2 x) e^{s i n (x)})

(3 x^{2} + 2) e^{s i n (x)} + e^{s i n (x)} cos (x) (x^{3} + 2 x)

Solution steps

\frac{d}{d x} ((x^{3} + 2 x) e^{s i n (x)})

Apply the Product Rule:

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

f = x^{3} + 2 x, g = e^{s i n (x)}

= \frac{d}{d x} (x^{3} + 2 x) e^{s i n (x)} + \frac{d}{d x} (e^{s i n (x)}) (x^{3} + 2 x)

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

\frac{d}{d x} (e^{s i n (x)}) = e^{s i n (x)} cos (x)

= (3 x^{2} + 2) e^{s i n (x)} + e^{s i n (x)} cos (x) (x^{3} + 2 x)

f (x) = - \frac{1}{3} t^{3} + 64 t + 3000

y^{^{'}} = \frac{1 - y ^{2}}{y}

\int \frac{( x - 7 )}{x ^{2} - 18 x + 82} d x

x^{2} + 25

\frac{1 + e ^{x}}{1 - e ^{x}}

What is the derivative of (x^3+2xe^{sin(x)}) ?
The derivative of (x^3+2xe^{sin(x)}) is (3x^2+2)e^{sin(x)}+e^{sin(x)}cos(x)(x^3+2x)
What is the first derivative of (x^3+2xe^{sin(x)}) ?
The first derivative of (x^3+2xe^{sin(x)}) is (3x^2+2)e^{sin(x)}+e^{sin(x)}cos(x)(x^3+2x)