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# Calculus Calculator

## Get detailed solutions to your math problems with our Calculus step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here.

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###  Difficult Problems

1

Here, we show you a step-by-step solved example of calculus. This solution was automatically generated by our smart calculator:

$\frac{d^2}{dx^2}\left(x^4+\sin\left(x\right)\right)$

The derivative of a sum of two or more functions is the sum of the derivatives of each function

$\frac{d}{dx}\left(x^4\right)+\frac{d}{dx}\left(\sin\left(x\right)\right)$

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$4x^{3}+\frac{d}{dx}\left(\sin\left(x\right)\right)$

The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if ${f(x) = \sin(x)}$, then ${f'(x) = \cos(x)\cdot D_x(x)}$

$4x^{3}+\cos\left(x\right)$
2

Find the ($1$) derivative

$4x^{3}+\cos\left(x\right)$

The derivative of a sum of two or more functions is the sum of the derivatives of each function

$\frac{d}{dx}\left(4x^{3}\right)+\frac{d}{dx}\left(\cos\left(x\right)\right)$

The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

$4\frac{d}{dx}\left(x^{3}\right)+\frac{d}{dx}\left(\cos\left(x\right)\right)$

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$4\cdot 3x^{2}+\frac{d}{dx}\left(\cos\left(x\right)\right)$

The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if $f(x) = \cos(x)$, then $f'(x) = -\sin(x)\cdot D_x(x)$

$4\cdot 3x^{2}-\sin\left(x\right)$

Multiply $4$ times $3$

$12x^{2}-\sin\left(x\right)$
3

Find the ($2$) derivative

$12x^{2}-\sin\left(x\right)$

##  Final answer to the problem

$12x^{2}-\sin\left(x\right)$

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