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Popular >

derivative of c+x+{f}(x(x)^2)

Solution

\frac{d}{d x} (c + x + f (x) (x)^{2})

Solution

x^{2} \frac{d}{d x} (f (x)) + 2 x f (x) + 1

Solution steps

\frac{d}{d x} (c + x + f (x) (x)^{2})

Apply the Sum/Difference Rule:

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

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

\frac{d c}{d x} = 0

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

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

= 0 + 1 + \frac{d}{d x} (f (x)) x^{2} + 2 x f (x)

Simplify

= x^{2} \frac{d}{d x} (f (x)) + 2 x f (x) + 1

Popular Examples

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

\int \frac{( 3 \cdot 2 ^{x} - 2 \cdot 3 ^{x} )}{2 ^{x}} d x

derivative of y=3(x^2-x+1)(5x-3)derivative of

y = 3 (x^{2} - x + 1) (5 x - 3)

(\partial)/(\partial x)((x+y^2)^3)

\frac{\partial}{\partial x} ((x + y^{2})^{3})

tangent of 4/x ,\at x=-5 tangent of

\frac{4}{x}, at x = - 5

integral of 5xcos(3x)

\int 5 x cos (3 x) d x

Frequently Asked Questions (FAQ)

What is the derivative of c+x+{f}(x(x)^2) ?
The derivative of c+x+{f}(x(x)^2) is x^2 derivative of {f}(x)+2x{f}(x)+1
What is the first derivative of c+x+{f}(x(x)^2) ?
The first derivative of c+x+{f}(x(x)^2) is x^2 derivative of {f}(x)+2x{f}(x)+1