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Popular >

derivative of (x^2-5/4 e^x)

Solution

\frac{d}{d x} ((x^{2} - \frac{5}{4}) e^{x})

Solution

2 x e^{x} + e^{x} (x^{2} - \frac{5}{4})

Solution steps

\frac{d}{d x} ((x^{2} - \frac{5}{4}) e^{x})

Apply the Product Rule:

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

f = x^{2} - \frac{5}{4}, g = e^{x}

= \frac{d}{d x} (x^{2} - \frac{5}{4}) e^{x} + \frac{d}{d x} (e^{x}) (x^{2} - \frac{5}{4})

\frac{d}{d x} (x^{2} - \frac{5}{4}) = 2 x

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

= 2 x e^{x} + e^{x} (x^{2} - \frac{5}{4})

Popular Examples

(\partial)/(\partial x)(sin(x^2*y^2))

\frac{\partial}{\partial x} (sin (x^{2} \cdot y^{2}))

x^2(dy)/(dx)+2xy=ln(x)

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

integral of (3x)/(x^2-2)

\int \frac{3 x}{x ^{2} - 2} d x

integral of (5x^2+3x^{-2})

\int (5 x^{2} + 3 x^{- 2}) d x

implicit (dy)/(dx),(cos(pix)+sin(piy))^5=23 implicit derivative

\frac{d y}{d x}, (cos (π x) + sin (π y))^{5} = 23

Frequently Asked Questions (FAQ)

What is the derivative of (x^2-5/4 e^x) ?
The derivative of (x^2-5/4 e^x) is 2xe^x+e^x(x^2-5/4)
What is the first derivative of (x^2-5/4 e^x) ?
The first derivative of (x^2-5/4 e^x) is 2xe^x+e^x(x^2-5/4)