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Popular >

derivative of f(x)=x^3+e^{4x}x^2

Solution

derivative of

f (x) = x^{3} + e^{4 x} x^{2}

Solution

3 x^{2} + e^{4 x} \cdot 4 x^{2} + 2 x e^{4 x}

Solution steps

\frac{d}{d x} (x^{3} + e^{4 x} x^{2})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{3}) + \frac{d}{d x} (e^{4 x} x^{2})

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

\frac{d}{d x} (e^{4 x} x^{2}) = e^{4 x} \cdot 4 x^{2} + 2 x e^{4 x}

= 3 x^{2} + e^{4 x} \cdot 4 x^{2} + 2 x e^{4 x}

Popular Examples

integral of 1/(x^2-6x+10)

\int \frac{1}{x ^{2} - 6 x + 10} d x

derivative of x^3+(3-3x^2^2+4)

\frac{d}{d x} (x^{3} + (3 - 3 x^{2})^{2} + 4)

(dy)/(dx)+y=x^2-2

\frac{d y}{d x} + y = x^{2} - 2

limit as x approaches 2 of sin((pix)/2)

x \to 2 lim (sin (\frac{π x}{2}))

integral of 1/(u^{3/2)}

\int \frac{1}{u ^{\frac{3}{2}}} d u

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=x^3+e^{4x}x^2 ?
The derivative of f(x)=x^3+e^{4x}x^2 is 3x^2+e^{4x}*4x^2+2xe^{4x}
What is the first derivative of f(x)=x^3+e^{4x}x^2 ?
The first derivative of f(x)=x^3+e^{4x}x^2 is 3x^2+e^{4x}*4x^2+2xe^{4x}