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Popular >

derivative of 5e^xtan(x)

Solution

derivative of

5 e^{x} tan (x)

Solution

5 (e^{x} tan (x) + sec^{2} (x) e^{x})

Solution steps

\frac{d}{d x} (5 e^{x} tan (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (e^{x} tan (x))

Apply the Product Rule:

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

f = e^{x}, g = tan (x)

= 5 (\frac{d}{d x} (e^{x}) tan (x) + \frac{d}{d x} (tan (x)) e^{x})

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

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

= 5 (e^{x} tan (x) + sec^{2} (x) e^{x})

Popular Examples

integral of (4x^2+3x-1)/(x^3-x^2)

\int \frac{4 x ^{2} + 3 x - 1}{x ^{3} - x ^{2}} d x

(\partial)/(\partial y)(y/(x+z))

\frac{\partial}{\partial y} (\frac{y}{x + z})

integral of (2x+1)/(x+1)

\int \frac{2 x + 1}{x + 1} d x

tangent of f(x)= 3/(x^2)tangent of

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

(\partial)/(\partial x)(((a+cx))/(c+b))

\frac{\partial}{\partial x} (\frac{( a + c x )}{c + b})

Frequently Asked Questions (FAQ)

What is the derivative of 5e^xtan(x) ?
The derivative of 5e^xtan(x) is 5(e^xtan(x)+sec^2(x)e^x)
What is the first derivative of 5e^xtan(x) ?
The first derivative of 5e^xtan(x) is 5(e^xtan(x)+sec^2(x)e^x)